Topics in Algebraic Topology and its Applications I
This is a series of courses on selected important topics in algebraic topology, which aims to help the research of the graduate students and junior researchers in pure and applied algebraic topology. During this semester, our selected topics will concentrate on Leray-Serre spectral sequence and its relevant topics, consisting of Barratt-Gugenheim-Moore simplicial fibre bundles theory, simplicial approach to the Leray-Serre spectral sequence with its comparison with the classical approach in the textbooks, sampling computations of spectral sequences performed by participated students, the applications in computing homotopy groups, Witten’s twisted de Rham cohomology with its comparison with Brown’s twisted tensor products, Grigor’yan-Muranov-Yau’s delta-cohomology and Delta-twisted homology.
讲师
日期
2024年09月10日 至 12月31日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 17:05 - 20:55 | A3-4-301 | ZOOM 06 | 537 192 5549 | BIMSA |
修课要求
Algebraic Topology
课程大纲
1. Homology with local coefficients
2. Exact couples
3. Homology of fibre spaces: Elementary Theory
4. Homology of fibre spaces
5. Computations of homology using Leray-Serre spectral sequence by examples
6. Brown twisted tensor, Witten’s twisted de Rham cohomology
7. Simplicial fibration/fibre bundles, twisted homology
8. Computations of homology using Leray-Serre spectral sequence or twisted (co-)homology by examples
2. Exact couples
3. Homology of fibre spaces: Elementary Theory
4. Homology of fibre spaces
5. Computations of homology using Leray-Serre spectral sequence by examples
6. Brown twisted tensor, Witten’s twisted de Rham cohomology
7. Simplicial fibration/fibre bundles, twisted homology
8. Computations of homology using Leray-Serre spectral sequence or twisted (co-)homology by examples
参考资料
1. George W. Whitehead, Elements of Homotopy Theory, Springer New York, NY eBook ISBN 978-1-4612-6318-0 published 2012
2. Robert M. Switzer, Algebraic Topology - Homotopy and Homology, Springer Berlin, Heidelberg. eBook ISBN 978-3-642-61923-6 published 2017
3. John McCleary, A User's Guide to Spectral Sequences, Cambridge University Press, 2000 ISBN-13 978-0521567596
2. Robert M. Switzer, Algebraic Topology - Homotopy and Homology, Springer Berlin, Heidelberg. eBook ISBN 978-3-642-61923-6 published 2017
3. John McCleary, A User's Guide to Spectral Sequences, Cambridge University Press, 2000 ISBN-13 978-0521567596
听众
Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
不公开
语言
中文
讲师介绍
BIMSA研究员，美国罗切斯特大学数学系博士，加州大学伯克利分校数学研究所博士后，前新加坡国立大学数学系终身教授，2021年12月入职北京雁栖湖应用数学研究院（BIMSA）。研究方向为代数拓扑与应用拓扑，在代数拓扑理论研究上的主要成就是建立了同伦群与辫子群理论的基础性关系，以及回路空间同伦论与置换群模表示论的基础性关系；在应用拓扑方面，将代数拓扑理论应用在大数据等领域并取得了一系列成果。在Journal of American Mathematical Society, Advances in Mathematics等数学顶尖期刊发表学术论文90余篇。2007年获得新加坡国家科学奖。2014年获得国家自然科学基金海外联合基金（杰青B）的资助。