On the group of homotopy equivalences of a manifold

Baues, Hans

doi:10.1090/S0002-9947-96-01555-3

On the group of homotopy equivalences of a manifold
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by Hans Joachim Baues

Trans. Amer. Math. Soc. 348 (1996), 4737-4773

DOI: https://doi.org/10.1090/S0002-9947-96-01555-3

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Abstract:

We consider the group of homotopy equivalences $\mathcal E(M)$ of a simply connected manifold $M$ which is part of the fundamental extension of groups due to Barcus-Barratt. We show that the kernel of this extension is always a finite group and we compute this kernel for various examples. This leads to computations of the group $\mathcal E(M)$ for special manifolds $M$, for example if $M$ is a connected sum of products $S^n\times S^m$ of spheres. In particular the group $\mathcal E(S^n\times S^n)$ is determined completely. Also the connection of $\mathcal E(M)$ with the group of isotopy classes of diffeomorphisms of $M$ is studied.

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