BIMSA > Jie Wu
Professor Jie Wu

Group: Algebraic Topology and its Applications

Office: A3-4-311

Email: wujie@bimsa.cn

Research Field: Algebraic Topology and its Application

Webpage: https://www.bimsa.cn/detail/jiewu.html

Biography

Jie Wu received a Ph.D. degree in Mathematics from the University of Rochester and worked as a postdoc at Mathematical Sciences Research Institute (MSRI), University of California, Berkeley. He was a former tenured professor at the Department of Mathematics, National University of Singapore. In December 2021, he joined the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA). His research interests are algebraic topology and applied topology. The main achievements in algebraic topology are to establish the fundamental relations between homotopy groups and the theory of braids, and the fundamental relations between loop spaces and modular representation theory of symmetric groups. In terms of applied topology, he has obtained various important results on topological approaches to data science. He has published more than 90 academic papers in top mathematics journals such as “the Journal of American Mathematical Society”, “Advances in Mathematics”, etc. In 2007, he won the "Singapore National Science Award”. In 2014, his project was funded by the “Overseas Joint Fund of National Natural Science Foundation” (Jieqing B).

Research Interest

  • Algebraic Topology: unstable homotopy theory, simplicial and homotopy theory, configuration spaces.
  • Interested Areas of Applications of Topology: Data Science, Mathematical Biology, Machine Learning.
  • Computational and Applied Topology: Topological data analysis, topological robotics, topological distribued computing.
  • Algebra: Combinatorial group theory, modular representation theory of Lie powers.
  • Combinatorial Topology: high-dimensional structure of graphs, combinatorial homotopy theory.
  • Low Dimensional Topology: braid groups, knots and links, geometric groups.

Education Experience

  • 1992 - 1995      University of Rochester      Mathematics      Doctor
  • 1986 - 1989      Nankai University      Mathematics      Master
  • 1980 - 1983      Lishui Normal College      Mathematics

Work Experience

  • 2021 -      BIMSA      Professor
  • 2019 - 2021      Hebei Normal University      Professor
  • 2009 - 2020      National University of Singapore      Professor
  • 2004 - 2008      National University of Singapore      Associate Professor
  • 1999 - 2004      National University of Singapore      Assistant Professor
  • 1997 - 1999      University of Pennsylvania      Lecturer
  • 1996 - 1997      University of Toronto and York University      Visiting Assistant Professor
  • 1995 - 1996      University of Californian, Berkeley      Postdoc
  • 1989 - 1992      Nankai University      Instructor

Honors and Awards

  • 2019      High-level Scientific Research Foundation of Hebei Province
  • 2014      Overseas Chinese Collaboration Fund, NSFC of China
  • 2011      Academic Research Fund (AcRF) Tier 2, Minister of Education of Singapore
  • 2007      National Science Award      with Jon Berrick

Publication

  • [1] Campbell, H. E. A.; Selick, Paul; Wu, Jie, Tensor algebras over the Steenrod algebra, JOURNAL OF PURE AND APPLIED ALGEBRA, 228(2024), 12, Paper No. 107730-8 pp
  • [2] Zhang, Zhiguo and Li, Jingyan and Wu, Jie, Strong digital topological complexity of digital maps, TOPOLOGY AND ITS APPLICATIONS, 351(2024), 108934
  • [3] Liu, Xingwu and Theriault, Stephen and Wu, Jie and Yue, Yunguang, Algebraic topology and distributed computing, Foundations of Data Science, 6(2024), 2, 195-220
  • [4] Xiang Liu, Huitao Feng, Jie Wu, and Kelin Xia, Computing hypergraph homology, Foundations of Data Science, 6(2024), 2, 172-194
  • [5] Guo-Wei Wei, Jie Wu, Duc Nguyen, and Kelin Xia, Preface: special issue on recent advances in topological deep learning, Foundations of Data Science, 6(2024), 2, i-iii
  • [6] Huiying Gong, Hongxing Wang, Yu Wang, Shen Zhang, Xiang Liu, Shuang Wu, Jie Wu, Xiaomei Sun, Shougong Zhang, Shing-Tung Yau, and Rongling Wu, Topological change of soil microbiota networks for forest resilience under global warming, Physics of Life Reviews, 50, 228-251 (2024)
  • [7] Xiaoxi Lin,Yunpeng ZI, and Jie Wu, NEW ASPECTS OF ANALYZING AMYLOID FIBRILS, arXiv:2405.14370(2024)
  • [8] Wanying Bi, Xin Fu, Jingyan Li, and Jie Wu, Persistent Magnitude for the Quantitative Analysis of the Structure and Stability of Carboranes, Journal of Computational Biophysics and Chemistry, 23(2024), 6, 1-11
  • [9] Wanying Bi, Jingyan Li, and Jie Wu, The magnitude homology of a hypergraph, accepted by Homology Homotopy and Applications(2023)
  • [10] Shuang Wu, Xiang Liu, Ang Dong, Claudia Gragnoli, Christopher Griffin, Jie Wu, Shing-Tung Yau, and Rongling Wu, The metabolomic physics of complex diseases, Proceedings of the National Academy of Sciences of the United States of America, 120(2023), 42, e2308496120
  • [11] Ran Liu, Xiang Liu, and Jie Wu, Persistent Path-Spectral (PPS) Based Machine Learning for Protein−Ligand Binding Affinity Prediction, Journal of Chemical Information and Modeling, 63(2023), 3, 1066-1075
  • [12] Shiquan Ren, Jie Wu, Mengmeng Zhang, The Embedded Homology of Hypergraph Pairs, Journal of Knot Theory and Its Ramifications (2023)
  • [13] Dong Chen, Jian Liu, Jie Wu, Guo-Wei Wei, Feng Pan, and Shing-Tung Yau, Path Topology in Molecular and Materials Sciences, The Journal of Physical Chemistry Letters, 14(2023), 4, 954-964
  • [14] Jian Liu, Dong Chen, Feng Pan, and Jie Wu, Neighborhood Path Complex for the Quantitative Analysis of the Structure and Stability of Carboranes, Journal of Computational Biophysics and Chemistry, 22(2023), 4, 503-511
  • [15] Pengcheng Li, Jianzhong Pan and Jie Wu, On modular cohomotopy groups, Israel Journal of Mathematics, 253(2023), 2, 887-915
  • [16] Ren, Shiquan and Wu, Chengyuan and Wu, Jie, Random hypergraphs, random simplicial complexes and their Künneth-type formulae, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 32(2023), 13, Paper No. 2350075-34 pp
  • [17] Dong Chen, Jian Liu, Jie Wu, and Guo-Wei Wei, Persistent hyperdigraph homology and persistent hyperdigraph Laplacians, Foundations of Data Science, 5(2023), 4, 558-588
  • [18] Li Feng, Dengcheng Yang, Sinan Wu, Chengwen Xue, Mengmeng Sang, Xiang Liu, Jie Wu, Claudia Gragnoli, Christopher Griffin, Chen Wang, Shing-Tung Yau, and Rongling Wu, Network modeling and topology of aging, accepted by Physics Reports(2023)
  • [19] Jian Liu, Ke-Lin Xia, Jie Wu, Stephen Shing-Toung Yau, and Guo-Wei Wei, Biomolecular topology: modelling and analysis, Acta Mathematica Sinica, 38(2022), 10, 1901-1938
  • [20] Xiang Liu, Huitao Feng, Jie Wu, and Kelin Xia, Hom-complex-based machine learning (HCML) for the prediction of protein-protein binding affinity changes upon mutation, Journal of Chemical Information and Modeling, 62(2022), 17, 3961-3969
  • [21] Yunguang Yue; Xingwu Liu; Jie Wu; Fengchun Lei, A Topological Characterization to Arbitrary Resilient Asynchronous Complexity, Mathematics, 10(2022), 15, 1-20
  • [22] Valeriy G. Bardakov; Vladimir V. Vershinin; Jie Wu;, On homotopy braids, Forum Mathematicum, 34(2022), 2, 447-454
  • [23] Jian Liu, Dong Chen, Jingyan Li, and Jie Wu, Neighborhood hypergraph model for topological data analysis, Computational and Mathematical Biophysics, 10(2022), 1, 262-280
  • [24] Jelena Grbić, Jie Wu, Kelin Xia, and Guo-Wei Wei, Aspects of topological approaches for data science, Foundations of Data Science, 4(2022), 2, 165-216
  • [25] Xiang Liu, Huitao Feng, Jie Wu, and Kelin Xia, Dowker complex based machine learning (DCML) models for protein-ligand binding affinity prediction, PLoS computational biology, 18(2022), 4, 1-17
  • [26] Mengmeng Zhang, Jingyan Li and Jie Wu, The twisted homology of simplicial set, Acta Mathematica Sinica, 38(10), 1781-1802 (2022)
  • [27] Murillo, Aniceto; Wu, Jie, Topological complexity of the work map, Journal of Topology and Analysis, 13(2021), 1, 219-238
  • [28] Xiang Liu, Huitao Feng, Jie Wu and Kelin Xia, Persistent spectral hypergraph based machine learning (PSH-ML) for protein-ligand binding affinity prediction, Briefings in Bioinformatics, 22(2021), 5, 1-12
  • [29] Ren, Shiquan; Wu, Chengyuan; Wu, Jie, Computational tools in weighted persistent homology, Chinese Ann. Math. Ser. B, 42(2021), 2, 237-258
  • [30] Chen, Junda; Lü, Zhi; Wu, Jie, Orbit configuration spaces of small covers and quasi-toric manifolds, Sci. China Math., 64(2021), 1, 167-196
  • [31] Xiang Liu, Xiangjun Wang, Jie Wu, and Kelin Xia, Hypergraph based persistent cohomology (HPC) for molecular representations in drug design, Briefings in Bioinformatics, 22(2021), 5, 1-12
  • [32] Yue, Y.; Lei, F.; Liu, X.; Wu, J. Asynchronous Computability Theorem in Arbitrary Solo Models, Mathematics 2020, 8 (5), 757.
  • [33] Chengyuan Wu, Shiquan Ren, Jie Wu, Kelin Xia Weighted fundamental group, Bulletin of the Malaysian Mathematical Sciences Society, 43 (2020), 4065-4088.
  • [34] Ruizhi Huang and Jie Wu, Combinatorics of double loop suspensions, evaluation maps and Cohen groups, J. Math. Soc. Japan 72 (3) (2020) pp. 847-889.
  • [35] Huang, R., Wu, J. Exponential growth of homotopy groups of suspended finite complexes, Math. Z. 295 (2020), 1301-1321.
  • [36] Zhenyu Meng, D Vijay Anand, Yunpeng Lu, Jie Wu, and Kelin Xia, Weighted persistent homology for biomolecular data analysis, Scientific Reports, 10(2020), 1, 2079
  • [37] Chengyuan Wu, Shiquan Ren, Jie Wu, and Kelin Xia, Discrete Morse theory for weighted simplicial complexes, Topology Appl., 270(2020), 107038
  • [38] Wu, Chengyuan; Ren, Shiquan; Wu, Jie; Xia, Kelin, Magnus representation of genome sequences, Journal of Theoretical Biology , 480(2019), 104-111
  • [39] Yue, Yunguang; Wu, Jie; Lei, Fengchun The evolution of non-degenerate and degenerate rendezvous tasks, Topology Appl. 264 (2019), 187-200.
  • [40] Theriault, S.; Wu, J. Relative homotopy abelian H-spaces, Manuscripta Math. 159 (3-4) (2019), 301-319.
  • [41] Pavutnitskiy, Fedor; Wu, Jie, A simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensions, Algebr. Geom. Topol, 19(2019), 1, 77-108
  • [42] Huang, Ruizhi; Wu, Jie Cancellation and homotopy rigidity of classical functors, J. Lond. Math. Soc. (2) 99 (1) (2019), 225-248.
  • [43] Meng, Fengjuan; Wu, Jie; Zhao, Chunxiang Time-dependent global attractor for extensible Berger equation, J. Math. Anal. Appl. 469 (2) (2019), 1045-1069.
  • [44] Stephane Bressan, Jingyan Li, Shiquan Ren, and Jie Wu, The embedded homology of hypergraphs and applications, Asian Journal of Mathematics, 23(2019), 3, 479-500
  • [45] Manturov, Vassily O.; Wu, J. $G_n^k$-groups for simplicial complexes and the word problem on 𝐺^2(𝐾), J. Knot Theory Ramications 27 (13) (2018), 1842013, 5 pp.
  • [46] Theriault, Stephen; Wu, Jie, Anick spaces and Kac-Moody groups, Algebr. Geom. Topol. , 18(2018), 7, 4305-4328
  • [47] Liang, Liang; Li, Fengling; Lei, Fengchun; Wu, Jie Local uniqueness of certain geodesics related to Heegaard splittings J. Knot Theory Ramications 27 (9) (2018), 1842003, 9 pp.
  • [48] Cohen, Frederick R.; Mikhailov, Roman; Wu, Jie , A combinatorial approach to the exponents of Moore spaces, Math. Z. , 290(2018), 1-2, 289-305
  • [49] Ivanov, Sergei O.; Mikhailov, Roman; Wu, Jie Leibniz rule on higher pages of unstable spectral sequences, Proc. Edinb. Math. Soc. (2) 61 (1) (2018), 265-282.
  • [50] Musin, Oleg R.; Wu, Jie Cobordism classes of maps and covers for spheres, Topology Appl. 237 (2018), 21-25.
  • [51] Shiquan Ren, Chengyuan Wu, and Jie Wu, Weighted persistent homology, Rocky Mountain J. Math. , 48(2018), 8, 2661-2687
  • [52] Li, J. Y.; Vershinin, V. V.; Wu, J. , Twisted simplicial groups and twisted homology of categories, Homology Homotopy Appl., 19(2017), 2, 111-130
  • [53] Huang, Ruizhi; Wu, Jie On mod $p A_p$-spaces, Algebr. Geom. Topol. 17 (4) (2017), 2125-2144.
  • [54] Li, Zhi-guo; Lei, Feng-chun; Chen, Zhi; Wu, Jie On fundamental group of a certain class of welded knots Commun. Math. Res. 33 (2) (2017), 177-184.
  • [55] Ivanov, Sergei O.; Mikhailov, Roman; Wu, Jie Homotopy theory and generalized dimension subgroups, J. Algebra 484 (2017), 224-246.
  • [56] Wu, Jie; Yuan, Zihong Stable functorial decompositions of $F(\mathbb{R}^{𝑛+1}, j)^{+} \wedge_{\sum_j} X^{(j)}$, Algebr. Geom. Topol. 17 (2) (2017), 895-915.
  • [57] Li, Zhiguo; Lei, Fengchun; Wu, Jie On the unknotting number of a welded knot J. Knot Theory Ramications 26 (1) (2017), 1750004, 22 pp.
  • [58] Li, Fengling; Lei, Fengchun; Wu, Jie 3-manifold invariants derived from the intersecting kernels, Internat. J. Math. 27 (13) (2016), 1650109, 9 pp.
  • [59] Ivanov, Sergei O.; Mikhailov, Roman; Wu, Jie , On nontriviality of certain homotopy groups of spheres, Homology Homotopy Appl., 18(2016), 2, 337-344
  • [60] Gao, Man; Tan, Colin; Wu, Jie Loop homological invariants associated to real projective spaces, Topology Appl. 209 (2016), 275-288.
  • [61] Mikhailov, Roman; Wu, Jie On the metastable homotopy of mod 2 Moore spaces, Algebr. Geom. Topol. 16 (3) (2016), 1773-1797.
  • [62] Gao, Man; Wu, Jie Simplicial monoid actions and associated monoid constructions J. Homotopy Relat. Struct. 11 (2) (2016), 199-208.
  • [63] Lei, Fengchun; Wu, Jie; Zhang, Yu On intersecting subgroups of Brunnian link groups, Algebr. Geom. Topol. 16 (2) (2016), 1043-1061.
  • [64] Bardakov, V. G.; Mikhailov, R.; Vershinin, V. V.; Wu, J. On the pure virtual braid group $VP_3$, Comm. Algebra 44 (3) (2016), 1350-1378.
  • [65] Grbi´c, Jelena; Panov, Taras; Theriault, Stephen; Wu, Jie, The homotopy types of momentangle complexes for flag complexes, Trans. Amer. Math. Soc., 368(2016), 9, 6663-6682
  • [66] Bardakov, V.; Gongopadhyay, K.; Singh, M.; Vesnin, A.; Wu, J. Some problems on knots, braids, and automorphism groups, Sib. Elektron. Mat. Izv.12 (2015), 394-405.
  • [67] Fang, Fuquan; Lei, Fengchun; Wu, Jie The symmetric commutator homology of link towers and homotopy groups of 3-manifolds, Commun. Math. Stat. 3 (4) (2015), 497-526.
  • [68] Beben, Piotr; Wu, Jie, The homotopy type of a Poincar´e duality complex after looping, Proc. Edinb. Math. Soc. (2) , 58(2015), 3, 581-616
  • [69] Wu, Jie Groups with structures and homotopy groups, Handbook of group actions. Vol. II, 371–396, Adv. Lect. Math. (ALM), 32, Int. Press, Somerville, MA, 2015.
  • [70] Li, J. Y.; Vershinin, V. V.; Wu, J. , Brunnian braids and Lie algebras, J. Algebra, 439(2015), 270-293
  • [71] Grbi´c, J.; Wu, J., On homotopy rigidity of the functor $\Sigma\Omega$ on co-H-spaces, Adv. Math., 273(2015), 523-539
  • [72] Bardakov, V. G.; Vershinin, V. V.; Wu, J. On Cohen braids, Published in Russian in Tr. Mat. Inst. Steklova 286 (2014), 22–39. Proc. Steklov Inst. Math. 286 (1) (2014), 16-32.
  • [73] Lei, Fengchun; Li, Fengling; Wu, Jie, On simplicial resolutions of framed links, Trans. Amer. Math. Soc., 366(2014), 6, 3075-3093
  • [74] Grbi´c, Jelena; Theriault, Stephen; Wu, Jie Suspension splittings and James-Hopf invariants, Proc. Roy. Soc. Edinburgh Sect. A 144 (1) (2014), 87-108.
  • [75] Berrick, A. J.; Hanbury, E.; Wu, J., Delta-structures on mapping class groups and braid groups, Trans. Amer. Math. Soc., 366(2014), 4, 1879-1903
  • [76] Chen, Weidong; Wu, Jie Decomposition of loop spaces and periodic problem on $\pi_*$, Algebr. Geom. Topol. 13 (6) (2013), 3245-3260.
  • [77] Gao, Man; Wu, Jie Homology decompositions of the loops on 1-stunted Borel constructions of $C^2$-actions, Algebr. Geom. Topol. 13 (6) (2013), 3175-3201.
  • [78] Berrick, A. J.; Hanbury, E.; Wu, J. Brunnian subgroups of mapping class groups and braid groups, Proc. Lond. Math. Soc. (3) 107 (4) (2013), 875-906.
  • [79] Vu, Dzh.(Wu, Jie); Mikhailov, R. V. Homotopy groups as centers of finitely presented groups (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 77 (3) (2013), 149-162; translation in Izv. Math. 77 (3) (2013), 581-593.
  • [80] Grbi´c, Jelena; Harper, John; Mimura, Mamoru; Theriault, Stephen; Wu, Jie, Rank $p−1$ mod $pH$-spaces, Israel J. Math, 194(2013), 2, 641-688
  • [81] Mikhailov, Roman; Wu, Jie , Combinatorial group theory and the homotopy groups of finite complexes, Geom. Topol., 17(2013), 1, 235-272
  • [82] Beben, Piotr; Wu, Jie Modular representations and the homotopy of low rank $P$-local CW complexes, Math. Z. 273 (3-4) (2013), 735-751.
  • [83] Grbi´c, J.; Theriault, S.; Wu, J. Decompositions of looped co-H-spaces, Proc. Amer. Math. Soc. 141 (4) (2013), 1451-1464.
  • [84] Bardakov, Valery G.; Mikhailov, Roman; Vershinin, Vladimir V.; Wu, Jie, Brunnian braids on surfaces, Algebr. Geom. Topol., 12(2012), 3, 1607-1648
  • [85] Cohen, F. R.; Wu, J. Artin’s braid groups, free groups, and the loop space of the 2-sphere, Q. J. Math. 62 (4) (2011), 891-921.
  • [86] Li, J. Y.; Lei, F. C.; Wu, J. Module structure on Lie powers and natural coalgebra-split sub-Hopf algebras of tensor algebras, Proc. Edinb. Math. Soc. (2) 54 (2) (2011), 467-504.
  • [87] Lei, Fengchun; Wu, Jie The intersecting kernels of Heegaard splittings, Algebr. Geom. Topol. 11 (2) (2011), 887-908.
  • [88] Li, J. Y.; Wu, J., On symmetric commutator subgroups, braids, links and homotopy groups, Trans. Amer. Math. Soc., 363(2011), 7, 3829-3852
  • [89] Selick, Paul; Theriault, Stephen; Wu, Jie, Functorial homotopy decompositions of looped co-H spaces, Math. Z. , 267(2011), 1-2, 139-153
  • [90] Mikhailov, Roman; Passi, Inder Bir S.; Wu, Jie Symmetric ideals in group rings and simplicial homotopy, J. Pure Appl. Algebra 215 (5) (2011), 1085-1092.
  • [91] J. Wu, The functor A^{min} for (p-1)-cell complexes and EHP sequences, Israel J. Math. , 178(2010), 349-391
  • [92] Wu, Jie Simplicial objects and homotopy groups. Braids, 31–181, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 19, World Sci. Publ., Hackensack, NJ, 2010.
  • [93] Mikhailov, Roman; Wu, Jie On homotopy groups of the suspended classifying spaces, Algebr. Geom. Topol. 10 (1) (2010), 565-625.
  • [94] Li, Jingyan; Wu, Jie Artin braid groups and homotopy groups Proc. Lond. Math. Soc. (3) 99 (3) (2009), 521-556.
  • [95] Cohen, F. R.; Wu, J. On braid groups and homotopy groups, Groups, homotopy and configuration spaces, 169-193, Geom. Topol. Monogr., 13, Geom. Topol. Publ., Coventry, 2008.
  • [96] Cohen, F. R.; Pakianathan, J.; Vershinin, V. V.; Wu, J. Basis-conjugating automorphisms of a free group and associated Lie algebras, Groups, homotopy and configuration spaces, 147-168, Geom. Topol. Monogr., 13, Geom. Topol. Publ., Coventry, 2008.
  • [97] Grbi´c, Jelena; Selick, Paul; Wu, Jie The decomposition of the loop space of the mod 2 Moore space, Algebr. Geom. Topol. 8 (2) (2008), 945-951.
  • [98] Selick, P.; Wu, J. Some calculations of Lie $(𝑛)^{max}$ for low 𝑛, J. Pure Appl. Algebra 212 (11) (2008), 2570-2580.
  • [99] Grbi´c, Jelena; Wu, Jie Applications of combinatorial groups to Hopf invariant and the exponent problem, Algebr. Geom. Topol. 6 (2006), 2229-2255.
  • [100] Grbi´c, Jelena; Wu, Jie Natural transformations of tensor algebras and representations of combinatorial groups, Algebr. Geom. Topol. 6 (2006), 2189-2228.
  • [101] Selick, P.; Theriault, S.; Wu, J. Functorial decompositions of looped coassociative co-H spaces, Canad. J. Math. 58 (4) (2006), 877-896.
  • [102] Selick, Paul; Wu, Jie The functor Amin on 𝑝-local spaces, Math. Z. 253 (3) (2006), 435-451.
  • [103] Jie Wu, On maps from loop suspensions to loop spaces and the shuffle relations on the Cohen groups, Mem. Amer. Math. Soc. 180, no. 851, vi+64 pp.(2006)
  • [104] Berrick, A. J.; Cohen, F. R.; Wong, Y. L.; Wu, J., Configurations, braids, and homotopy groups, J. Amer. Math. Soc., 19(2006), 2, 265-326
  • [105] Cohen, F. R.; Wu, J. On braid groups, free groups, and the loop space of the 2-sphere, Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), 93-105, Progr. Math., 215, Birkh?user, Basel, 2004.
  • [106] Selick, Paul; Wu, Jie On functorial decompositions of self-smash products, Manuscripta Math. 111 (4) (2003), 435-457.
  • [107] Jie Wu, Homotopy theory of the suspensions of the projective plane, 162, no. 769, x+130 pp.(2003)
  • [108] Wu, Jie On co-𝐻-maps to the suspension of the projective plane, Topology Appl. 123 (3) (2002), 547-571.
  • [109] Wu, Jie A braided simplicial group, Proc. London Math. Soc. (3) 84 (3) (2002), 645-662.
  • [110] Wu, Jie; Gerstenhaber, Murray; Stasheff, James On the Hodge decomposition of differential graded bi-algebras, J. Pure Appl. Algebra 162 (1) (2001), 103-125.
  • [111] Jie Wu, Combinatorial descriptions of homotopy groups of certain spaces, Math. Proc. Cambridge Philos. Soc., 130(2001), 3, 489-513
  • [112] Wu, Jie On products on minimal simplicial sets, J. Pure Appl. Algebra 148 (1) (2000), 89-111.
  • [113] Selick, Paul; Wu, Jie, On natural coalgebra decompositions of tensor algebras and loop suspensions, Mem. Amer. Math. Soc. 148, no. 701, viii+109 pp.(2000)
  • [114] Wu, Jie On the homology of configuration spaces $C(((M,M_0)\times \mathbb{R}^n;X)$. Math. Z. 229 (2) (1998), 235-248.
  • [115] Wu, Jie On combinatorial calculations for the James-Hopf maps, Topology 37 (5) (1998), 1011-1023.
  • [116] Wu, Jie A product decomposition of $\Omega_0^3\sum\mathbb{R}P^2$, Topology 37 (5) (1998), 1025-1030.
  • [117] Wu, Jie On fibrewise simplicial monoids and Milnor-Carlsson’s constructions, Topology 37(5) (1998), 1113-1134.
  • [118] Cohen, F. R.; Wu, Jie A remark on the homotopy groups of $\sum^n\mathbb{R}P^2$. The Cech centennial ˇ(Boston, MA, 1993), 65-81, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995.
  • [119] Wu, Jie Homology of stable function spaces, (Chinese) Acta Math. Sinica 34 (5) (1991),703-709.

 

Update Time: 2024-09-12 17:18:04