Research-Rational Self-closeness Numbers of Mapping Spaces

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Rational Self-closeness Numbers of Mapping Spaces

Speaker: Yichen Tong (Kyoto University)
Time: Dec 19, 2022, 16:20-17:20
Location: Tencent Meeting ID 402-5413-1062

Abstract

For a closed simply-connected 2n-dimensional manifold M, it has been proved that the components of the free mapping space from M to 2n-sphere have exactly two different rational homotopy types. However, since this result is proved by algebraic models of components, we do not know whether other homotopy invariants distinguish these two types or not. In this talk, we completely determine the self-closeness numbers of rationalized components of the mapping space and prove that they do distinguish different rational homotopy types. The methods also have potential to be extended on other mapping spaces.