北京雁栖湖应用数学研究院

阮洋洋

黄瑞芝

2025年11月13日 11:00 至 12:00

A3-2-303

Zoom 204 323 0165 (BIMSA)

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincaré duality complexes in which a loop of a product of spheres appears as a direct summand. This decomposition is further applied to derive results on local hyperbolicity, on inertness and non-inertness, on the gaps between rational inertness and local or integral inertness, and on the homotopy theory of smooth manifolds with transversally embedded spheres. In particular, in every dimension greater than three, there exist infinitely many finite $CW$-complexes, pairwise non-homotopy-equivalent, whose loop spaces retract off the loops of their lower skeletons rationally but not locally, and whose top cell attachments produce infinitely many new torsion homotopy groups with exponentially growing ranks.

黄瑞芝于2017底在新加坡国立大学获数学博士学位，之后在中国科学院数学与系统科学研究院工作至今。主要研究代数拓扑及其在流形拓扑、微分几何与数学物理中的应用。研究成果发表于Adv. Math., Tran. AMS, J. Lon. Math. Soc, Annales l'Institut Fourier, Math. Z.等数学期刊。