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

Broughton, S. Allen

doi:10.1090/S0002-9939-1991-1041012-1

The Gottlieb group of finite linear quotients of odd-dimensional spheres
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by S. Allen Broughton

Proc. Amer. Math. Soc. 111 (1991), 1195-1197

DOI: https://doi.org/10.1090/S0002-9939-1991-1041012-1

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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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