Some Results on Pseudo-Collar Structures on High-Dimensional Manifolds

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.