Rank conditions for finite group actions on 4-manifolds

Abstract

Let M be a closed, connected, orientable topological $4$ -manifold, and G be a finite group acting topologically and locally linearly on M. In this paper, we investigate the spectral sequence for the Borel cohomology $H^*_G(M)$ and establish new bounds on the rank of G for homologically trivial actions with discrete singular set.

Finite group actions on 4-manifolds and equivariant bundles

“…We are mainly interested in comparing smooth actions with those which are topological and locally linear, but important examples arise for symplectic 4-manifolds and complex surfaces. Here is a sampling of survey articles and recent work on aspects of this general theme: [1,2,3,5,6,7,10,15,22,20,21,23,26,31,36]. We will focus on the existence and classification of equivariant bundles, and their applications in Yang-Mills gauge theory to the study of finite group actions.…”