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On the homotopy groups of the self-equivalences of linear spheres

Published online by Cambridge University Press:  26 October 2015

Assaf Libman
Assaf Libman*
Affiliation:
Institute of Mathematics, University of Aberdeen, Fraser Noble Building, Aberdeen AB24 3UE, UK ([email protected])
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Abstract

Let S(V) be a complex linear sphere of a finite group G. Let S(V)*n denote the n-fold join of S(V) with itself and let aut G(S(V)*) denote the space of G-equivariant self-homotopy equivalences of S(V)*n. We show that for any k ≥ 1 there exists M > 0 that depends only on V such that |πk autG(S(V)*n)|≤ M for all n ≫0.

Keywords

homotopy groupsself-equivalencesequivariant spherescomplex representationsPrimary 55Q5255P9155N91
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 445 - 462
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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