Groups that act pseudofreely on S² ×S²

Michael P. McCooey

Vol. 230 (2007), No. 2, 381–408

DOI: 10.2140/pjm.2007.230.381

Abstract

A pseudofree group action on a space X is one whose set of singular orbits forms a discrete subset of its orbit space. Equivalently — when G is finite and X is compact — the set of singular points in X is finite. In this paper, we classify all of the finite groups which admit pseudofree actions on S² × S². The groups are exactly those that admit orthogonal pseudofree actions on S² × S² ⊂ ℝ³ × ℝ³, and they are explicitly listed.

This paper can be viewed as a companion to a preprint of Edmonds, which uniformly treats the case in which the second Betti number of a four-manifold M is at least three.

Keywords

pseudofree, group, group action, four-manifold

Mathematical Subject Classification 2000

Primary: 55M35, 57S25, 57S17

Secondary: 20J06, 55T10

Milestones

Received: 1 November 2004

Accepted: 18 March 2007

Published: 1 April 2007