Date of Award

December 2014

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Craig Guilbault

Committee Members

Ric Ancel, Chris Hruska, Allen Bell, Suzanne Boyd, Craig Guilbault

Abstract

We are interested in contractible n-manifolds M which decompose or split as M = A union B where A,B, and A intersect B are all homeomorphic to Euclidean n-space or A,B, and A intersect B are all homeomorphic to the n-dimensional unit ball. We introduce a 4-manifold M containing a spine which splits as A union B with A,B, and A intersect B all collapsible which in turn implies M splits as the union of two 4-balls whose intersection is also a 4-ball. From M we obtain a countably infinite collection of distinct 4-manifolds all of which split this way. Connected sums at infinity of interiors of manifolds from sequences contained in this collection constitute an uncountable set of open 4-manifolds each of which splits as the union of two 4-spaces with intersection also a 4-space.

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