Smoothability of Z\times Z-actions on 4-manifolds

TL;DR

This paper constructs examples of Z×Z-actions on certain 4-manifolds that are topologically but not smoothly realizable, revealing new insights into smoothability in 4-dimensional topology.

Contribution

It provides explicit examples of nonsmoothable Z×Z-actions on connected sums involving Enriques surfaces, advancing understanding of smoothability obstructions.

Findings

Existence of nonsmoothable Z×Z-actions on specific 4-manifolds

Construction of nonsmoothable self-homeomorphisms on Enriques surfaces

Demonstration that generators can be smoothable despite the overall action being nonsmoothable

Abstract

We construct a nonsmoothable Z\times Z-action on the connected sum of an Enriques surface and S^2\times S^2, such that each of generators is smoothable. We also construct a nonsmoothable self-homeomorphism on an Enriques surface.