Finite group action and equivariant bordism

S. S. Khare

Vol. 116 (1985), No. 1, 39–44

DOI: 10.2140/pjm.1985.116.39

Abstract

Conner and Floyd proved that if Z₂^k acts on a closed manifold M differentiably and without any fixed point, then M is a boundary. Stong gave a stronger result proving that if (M,𝜃) is a closed Z₂^k-differential manifold with no stationary point, then (M,𝜃) is a Z₂^k-boundary. In the present note, we discuss this problem for a finite group in detail. Let G be a finite group. By the 2-central component G₂(C) of G, we will mean the subgroup of G consisting of the identity element and all the elements of order 2 in the center of G. We prove in this note that the fixed data of the 2-central component G₂(C) of G determines G-bordism.

Mathematical Subject Classification 2000

Primary: 57R85

Milestones

Received: 17 June 1983

Revised: 29 July 1983

Published: 1 January 1985