Semifree finite group actions on homotopy spheres

Ronald Dotzel

Vol. 103 (1982), No. 1, 25–27

DOI: 10.2140/pjm.1982.103.25

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 X^G is also homotopy equivalent to Sⁿ (as e.g., in Sⁿ × D^K) necessary and sufficent conditions are given to determine the degree of the inclusion X^G → 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