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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Gottlieb group of finite linear quotients of odd-dimensional spheres


Author: S. Allen Broughton
Journal: Proc. Amer. Math. Soc. 111 (1991), 1195-1197
MSC: Primary 57S17; Secondary 55Q52, 57S25
MathSciNet review: 1041012
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Abstract: Let $ G$ be a finite, freely acting group of homeomorphisms of the odd-dimensional sphere $ {S^{2n - 1}}$. John Oprea has proven that the Gottlieb group of $ {S^{2n - 1}}/G$ equals $ Z(G)$, the centre of $ G$. The purpose of this short paper is to give a considerably shorter, more geometric proof of Oprea's theorem in the important case where $ G$ is a linear group.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1041012-1
PII: S 0002-9939(1991)1041012-1
Keywords: Gottlieb group, linear group actions
Article copyright: © Copyright 1991 American Mathematical Society