Absolutely exotic compact 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.
Keywords
Cite
@article{arxiv.1410.1461,
title = {Absolutely exotic compact 4-manifolds},
author = {Selman Akbulut and Daniel Ruberman},
journal= {arXiv preprint arXiv:1410.1461},
year = {2014}
}
Comments
New title reflecting major revision; the main theorem now converts any relatively exotic manifold into an absolutely exotic one, and yields homotopy equivalent manifolds not equivalent rel boundary. 21 pages, 13 figures, some in color