Vol. 103, No. 1, 1982

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Semifree finite group actions on homotopy spheres

Ronald Dotzel

Vol. 103 (1982), No. 1, 25–27
Abstract

Suppose G is a finite group acting semifreely (i.e., free off the fixed set) on a finite CW complex X in the homotopy type of Sn. When XG is also homotopy equivalent to Sn (as e.g., in Sn × DK) necessary and sufficent conditions are given to determine the degree of the inclusion XG X. It follows that for instance, if G is the group of quaternions (nonabelian of order 8), the only attainable degrees are those ±1 (mod 8).

Mathematical Subject Classification 2000
Primary: 57S25
Secondary: 57S17
Milestones
Received: 26 September 1980
Published: 1 November 1982
Authors
Ronald Dotzel