Nonsmoothable group actions on spin 4-manifolds

TL;DR

The paper demonstrates that most closed, simply connected spin 4-manifolds admit certain group actions that are topologically possible but cannot be smoothed, highlighting differences between topological and smooth categories.

Contribution

It constructs nonsmoothable, homologically trivial, pseudofree actions of cyclic groups on spin 4-manifolds, excluding only S^4 and S^2×S^2.

Findings

Existence of nonsmoothable actions for large primes p

Such actions are homologically trivial and pseudofree

Applicable to all but two specific 4-manifolds

Abstract

We show that every closed, simply connected, spin topological 4-manifold except $S^4$ and $S^2\times S^2$ admits a homologically trivial, pseudofree, locally linear action of $\mathbb{Z}_p$ for any sufficiently large prime number $p$ which is nonsmoothable for any possible smooth structure.