Smooth structures on non-orientable four-manifolds and free involutions

TL;DR

This paper explores the existence of exotic smooth structures on non-orientable 4-manifolds, introduces new examples via Gluck twists, and investigates orientation-reversing free involutions, expanding understanding of smooth topology in four dimensions.

Contribution

It provides new constructions of exotic smooth structures on non-orientable 4-manifolds and demonstrates the existence of exotic free involutions through analysis of 2-coverings.

Findings

New exotic smooth structures on non-orientable 4-manifolds

Existence of orientation-reversing exotic free involutions

Application of Gluck twists to generate exotic manifolds

Abstract

In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known constructions and provide new examples of exotic manifolds that are obtained as an application of Gluck twists to the standard smooth structure. Inspection of the smooth structure on the oriented 2-covers yields existence results of orientation-reversing exotic free involutions.