Equivariant deformations of manifolds and real representations

Davide L. Ferrario

Vol. 196 (2000), No. 2, 353–368

DOI: 10.2140/pjm.2000.196.353

Abstract

In the paper we give a partial answer to the following question: Let G be a finite group acting smoothly on a compact (smooth) manifold M, such that for each isotropy subgroup H of G the submanifold M^H fixed by H can be deformed without fixed points; is it true that then M can be deformed without fixed points G-equivariantly? The answer is no, in general. It is yes, for any G-manifold, if and only if G is the direct product of a 2-group and an odd-order group.

Milestones

Received: 19 November 1998

Published: 1 December 2000