Date of Award

May 2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Craig Guilbault

Committee Members

Frederic Ancel, Geoffrey Christopher Hruska, Jeb Willenbring, Ian Musson

Keywords

1-Sided H-Cobordism, Cobordism, Manifold, Plus Construction, Pseudo-Collar

Abstract

In this dissertation we outline a partial reverse to Quilen's plus construction in the high-dimensional manifold categor. We show that for any orientable manifold N with fundamental group Q and any fintely presented superperfect group S, there is a 1-sided s-cobordism (W, N, N-) with the fundamental group G of N- a semi-direct product of Q by S, that is, with G satisying 1 -> S -> G -> Q -> 1 and actually a semi-direct product.

We then use a free product of Thompson's group V with itself to form a superperfect group S and start with an orientable manifold N with fundamental group Z, the integers, and form semi-direct products of (S x S .... x S) with Z and cobordism (W1, N, N-), (W2, N-, N--), (W3, N--, N---) and so on and glue these 1-sided s-cobordisms together to form an uncoutable family of 1-ended pseudo-collarable manifolds V all with non-pro-isomorphic fundamental group systems at infinity.

Finally, we generalize a result of Guilbault and Tinsley to show that in M is a manifold with hypo-Abelian fundamental group with an element of infinite order, then there is an absolutely inward tame manifold V with boundary M which fails to be pseudo-collaarable.

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