Finite group actions on 4-manifolds and equivariant bundles

TL;DR

This paper establishes criteria for the existence of equivariant bundles on 4-manifolds with cyclic group actions, using twisted signature formulas to relate fixed point data and isotropy representations.

Contribution

It provides necessary and sufficient conditions for equivariant bundle existence on 4-manifolds under cyclic group actions, based on new congruence relations.

Findings

Derived conditions from twisted signature formula

Established congruence relations between fixed points and isotropy

Provided criteria for equivariant bundle existence

Abstract

Given a 4-manifold with a homologically trivial and locally-linear cyclic group action, we obtain necessary and sufficient conditions for the existence of equivariant bundles. The conditions are derived from the twisted signature formula and are in the form of congruence relations between the fixed point data and the isotropy representations.