Homotopy self-equivalences of manifolds

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• Ian Hambleton (McMaster University)
• Thursday 30 May 2024, 09:30-10:30
• External.

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TRH - Topology, representation theory and higher structures

For a closed, topological $n$-manifold $M$, let $E(M)$ denote its space of pointed self-homotopy equivalences. In [Hambleton-Kreck, 2004] a braid of interlocking exact sequences was established in order to obtain new information about  $Aut(M):=\pi_0(E(M))$, assuming that $M$ is a closed, oriented $4$-manifold and the self-equivalences are orientation-preserving. It seemed clear to the authors at the time that a similar braid should exist for higher dimensional manifolds.The aim of this project is to carry out the details of this extension, and to generalize the braid to include information about the higher homotopy groups $\pi_k(E(M))$ and related variants. This is a preliminary report on joint work with Kursat Sozer (McMaster) and Robin Sroka (Muenster).

This talk is part of the Isaac Newton Institute Seminar Series series.

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