Fixed sets of involutions

Frank Lewis Capobianco

Vol. 75 (1978), No. 2, 339–345

DOI: 10.2140/pjm.1978.75.339

Abstract

In their work Differentiable Periodic Maps, Conner and Floyd posed the following question: Given a closed smooth n-manifold Mⁿ, for what values of k does there exist a closed (n + k)-manifold V ^n+k with smooth involution T whose fixed point set is diffeomorphic to Mⁿ? In this paper we show that for many values of k there is a closed manifold with involution (T,V ^n+k) whose fixed point set is cobordant to Mⁿ.

Mathematical Subject Classification 2000

Primary: 57R85

Milestones

Received: 7 December 1976

Published: 1 April 1978