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On the group of homotopy equivalences of a manifold
Authors:Hans Joachim Baues
Affiliation:Max Planck Institute for Mathematics, Gottfried-Claren-Strasse 26, 53225 Bonn, Germany
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 $S^ntimes S^m$ of spheres. In particular the group $mathcal E(S^ntimes S^n)$ 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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