Rational self-closeness numbers of mapping spaces
演讲者
童浥尘
时间
2022年10月21日 10:30 至 11:30
地点
Online
线上
Zoom 293 812 9202
(BIMSA)
摘要
For spaces X and Y , let Map(X, Y ) denotes the free mapping space from X to Y . Classifying components up to homotopy type for a given mapping space is a classical problem in algebraic topology and has been studied since at least 1940s. For Map(M, S2n) where M a closed simply-connected 2n-dimensional manifold, it was proved that its components have exactly two rational homotopy types. However, since this result is proved by algebraic models of components, we do not know whether a rational homotopy invariant distinguishes these two types or not. In this talk, we completely determine the rational self-closeness numbers of components of Map(M, S2n) and prove that they do distinguish different rational homotopy types.