4-manifolds and intersection forms with local coefficients

TL;DR

This paper extends Donaldson's diagonalization theorem to intersection forms with specific local coefficients, leading to new examples of topological 4-manifolds that cannot be smoothed.

Contribution

It introduces a generalization of Donaldson's theorem for intersection forms with local coefficients, expanding the understanding of 4-manifold topology.

Findings

Extended Donaldson's theorem to local coefficient cases

Constructed new non-smoothable topological 4-manifolds

Provided constraints under which the extension holds

Abstract

We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.