Corks and automorphisms of 3-manifolds

TL;DR

This paper studies two contractible 3-manifolds with complex boundary symmetries, demonstrating that boundary diffeomorphisms extend to the entire manifold, thus showing they are not corks, using advanced 3- and 4-manifold techniques.

Contribution

It provides the first analysis of boundary mapping class groups for these specific contractible manifolds and shows boundary diffeomorphisms extend to the whole manifold, ruling out cork structures.

Findings

Boundary diffeomorphisms extend to the entire manifold

These manifolds are not corks due to boundary properties

Methods combine 3- and 4-manifold techniques

Abstract

We investigate two specific contractible manifolds (one Stein, and the other non-Stein) whose boundaries have non-trivial mapping class groups. In both cases we show that every diffeomorphism of their boundary extends to a diffeomorphism of the full manifold. In particular, these manifolds cannot be corks. The methods are a mix of 3 and 4-manifold techniques.