Rank conditions for finite group Actions on 4-Manifolds

TL;DR

This paper investigates the Borel spectral sequence in the context of finite group actions on 4-manifolds, establishing new bounds on the group rank for certain homologically trivial actions with discrete singular sets.

Contribution

It introduces new bounds on the rank of finite groups acting on 4-manifolds, focusing on homologically trivial actions with discrete singular sets, through analysis of the Borel spectral sequence.

Findings

Established bounds on the rank of finite groups acting on 4-manifolds.

Analyzed the Borel spectral sequence for equivariant cohomology.

Focused on homologically trivial actions with discrete singular sets.

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 Borel spectral sequence for the G-equivariant cohomology of M, and establish new bounds on the rank of G for homologically trivial actions with discrete singular set.