The converse to the Smith theorem for Z_p-homology spheres

Stephen Jeffrey Willson

Vol. 56 (1975), No. 2, 597–605

DOI: 10.2140/pjm.1975.56.597

Abstract

Let X be a finite CW complex with the Z_ρ homology of an n-sphere. Let Z_ρ act cellularly on X. The Smith theorem asserts that the fixed point set X^Z_ρ has the Z_ρ homology of an m-sphere for −1 ≦ m ≦ n. A converse to this Smith theorem is proved.

Mathematical Subject Classification

Primary: 57C35

Secondary: 57E15

Milestones

Received: 1 May 1974

Published: 1 February 1975