Spherical isotropy representations
type: Item
instance of: scholarly article
title: Spherical isotropy representations
zbMATH Open document ID: 0585.57020
DOI: 10.1007/BF02698806
author: Ted Petrie
author: John D. Randall
published in: Publications Mathématiques
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104009
review text: An old question of P. A. Smith considers a finite group G acting smoothly on a closed homotopy sphere \(\Sigma\) with \(\Sigma^ G\) consisting of precisely two points and asks whether the representations of G on the tangent spaces at the two fixed points are the same. This would be true, obviously, for a linear action on a sphere. For G abelian of odd order with at least four noncyclic Sylow subgroups this paper shows that the answer is no, providing proofs and elaboration of previously announced results. For a large family of representations one has necessary and sufficient conditions that two representations in the family occur as fixed point representation after stabilization.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 3938062
zbMATH Keywords: finite group actions on homotopy spheres
zbMATH Keywords: Smith equivalent fixed
zbMATH Keywords: points
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3938062