Absolutely exotic compact 4-manifolds
Selman Akbulut, Daniel Ruberman

TL;DR
This paper introduces a method to construct absolutely exotic smooth structures on compact 4-manifolds with boundary, including contractible ones, by modifying relatively exotic manifolds with homology cobordisms.
Contribution
It provides a novel technique to produce absolutely exotic structures on 4-manifolds, expanding the understanding of exotic smooth structures beyond relative cases.
Findings
Constructed absolutely exotic structures on compact 4-manifolds with boundary.
Extended the concept of exotic structures to absolute cases, independent of boundary parameterization.
Applied the method to corks to produce examples on contractible 4-manifolds.
Abstract
We show how to construct absolutely exotic smooth structures on compact 4-manifolds with boundary, including contractible manifolds. In particular, we prove that any compact smooth 4-manifold W with boundary that admits a relatively exotic structure contains a pair of codimension-zero submanifolds homotopy equivalent to W that are absolutely exotic copies of each other. In this context, {\em absolute} means that the exotic structure is not relative to a particular parameterization of the boundary. Our examples are constructed by modifying a relatively exotic manifold by adding an invertible homology cobordism along its boundary. Applying this technique to corks (contractible manifolds with a diffeomorphism of the boundary that does not extend to a diffeomorphism of the interior) gives examples of absolutely exotic smooth structures on contractible 4-manifolds.
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