Abstract

The classification of manifolds in various categories is a classical problem in topology. It has been widely investigated by applying techniques from geometric topology in the last century. However, the known results tell us very little information about the homotopy of manifolds. In the last ten years, there have been attempts to study the homotopy properties of manifolds by using techniques in unstable homotopy theory. In this talk, we will discuss the loop decomposition method in this topic and review the known results and our recent work.

Speaker

黄瑞芝，中国科学院数学与系统科学研究院副研究员。主要研究代数拓扑在其他领域中的应用，特别是流形及指标理论。他与段海豹及新加坡国立大学韩飞教授合作建立了复弦流形的代数拓扑理论，构造了一族广义Witten亏格，并证明其关于非交换群作用的消灭定理。其后，基于Witten-Freed-Hopkins关于数学物理中M理论的数学研究，他还与合作者合作构造了12维流形上6种不同的整三次型及其相应的anomalycancellation公式。

个人主页：

http://www.math.ac.cn/kyry/202203/t20220301_682769.html