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

Assaf Libman

doi:10.1017/S0013091515000127

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

Assaf Libman

Mathematical Science

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Abstract

Let S(V ) be a complex linear sphere of a finite group G. LetS(V )∗n denote the n-fold join of S(V ) with itself and let autG(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 which depends only onV such that |k autG(S(V )∗n)| ≤ M is for all n ≫ 0.

Original language	English
Pages (from-to)	445-462
Number of pages	18
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	59
Issue number	2
Early online date	26 Oct 2015
DOIs	https://doi.org/10.1017/S0013091515000127
Publication status	Published - May 2016

Keywords

homotopy groups
self-equivalences
equivariant spheres
complex representations

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Accepted Manuscript
This article has been published in a revised form in Proceedings of the Edinburgh Mathematical Society, DOI: https://doi.org/10.1017/S0013091515000127. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Edinburgh Mathematical Society 2016.
Accepted author manuscript, 234 KBLicence: Unspecified

Assaf Libman
- School of Natural & Computing Sciences, Mathematical Science - Reader
Person: Academic

Cite this

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AB - Let S(V ) be a complex linear sphere of a finite group G. LetS(V )∗n denote the n-fold join of S(V ) with itself and let autG(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 which depends only onV such that |k autG(S(V )∗n)| ≤ M is for all n ≫ 0.

KW - homotopy groups

KW - self-equivalences

KW - equivariant spheres

KW - complex representations

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EP - 462

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

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ER -

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

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