Gluck twisting 4-manifolds with odd intersection form

TL;DR

This paper establishes a simple criterion to determine when Gluck twisting an odd smooth 4-manifold along a 2-sphere preserves its diffeomorphism type, using handlebody and plug twisting techniques.

Contribution

It provides the strongest known condition under which Gluck twisting on odd 4-manifolds does not alter their diffeomorphism type, improving previous results.

Findings

A criterion for invariance under Gluck twisting on odd 4-manifolds.

Handlebody and plug twisting techniques applied to 4-manifold topology.

Enhanced understanding of the effect of Gluck twisting on odd homology classes.

Abstract

We give a simple criterion when a Gluck twisting an odd smooth 4-manifold along a 2-sphere $S\subset X$ does not change its diffeomorphism type. We obtain this by handlebody techniques and plug twisting operation, getting a slightly stronger version of the known fact that Gluck twisting of a 2-sphere $S\subset X$ of a compact smooth 4-manifold with an odd spherical class, in the complement of S, does not change the diffeomorphism type of X. This is the best possible result on Gluck twisting manifolds with odd homology classes.