Exotic Dehn twists and homotopy coherent group actions

TL;DR

This paper investigates extending cyclic group actions from the boundary to the interior of 4-manifolds, revealing that certain Dehn twists are infinite order exotic automorphisms in specific cases.

Contribution

It proves that Dehn twists along Seifert homology spheres are infinite order exotic automorphisms in positive-definite fillings, extending understanding of group actions on 4-manifolds.

Findings

Dehn twists along Seifert homology spheres are infinite order exotic automorphisms

Extension of cyclic group actions from boundary to interior is studied

Most positive-definite fillings admit such exotic automorphisms

Abstract

We consider the question of extending a smooth homotopy coherent finite cyclic group action on the boundary of a smooth 4-manifold to its interior. As a result, we prove that Dehn twists along any Seifert homology sphere, except the 3-sphere, on their simply connected positive-definite fillings are infinite order exotic.