This article is cited in 12 papers

Geometry and topology

On finite groups acting on spheres and finite subgroups of orthogonal groups

Bruno P. Zimmermann

Universit\`a degli Studi di Trieste, Dipartimento di Matematica e Informatica, 34127 Trieste, Italy

Abstract: This is a survey on old and new results as well as an introduction to various related basic notions and concepts, based on two talks given at the International Workshop on Geometry and Analysis in Kemerovo (Sobolev Institute of Mathematics, Kemerovo State University) and at the University of Krasnojarsk in June 2011. We discuss finite groups acting on low-dimensional spheres and homology spheres, comparing with the finite subgroups of the corresponding orthogonal groups, and also finite simple groups acting on spheres and homology spheres of arbitrary dimension.

Keywords: finite groups acting on spheres, finite subgroups of orthogonal groups, finite simple groups.

UDC: 515.146.34, 512.816

MSC: 57S17, 57S25, 20E32, 20F65

Received December 20, 2011, published January 24, 2012

Language: English