Characterization of pseudo-collarable manifolds with boundary

TL;DR

This paper provides a comprehensive characterization of pseudo-collarable manifolds with boundary for dimensions six and higher, extending previous work to include noncompact boundaries and non-stable fundamental groups at infinity.

Contribution

It extends the characterization of pseudo-collarable manifolds to include those with noncompact boundary and non-stable fundamental groups at infinity.

Findings

Complete characterization of pseudo-collarable manifolds with boundary for n≥6.

Extension of previous work to manifolds with noncompact boundary.

Applicable to manifolds with non-peripherally stable fundamental groups at infinity.

Abstract

In this paper we obtain a complete characterization of pseudo-collarable $n$-manifolds for $n\geq 6$. This extends earlier work by Guilbault and Tinsley to allow for manifolds with noncompact boundary. In the same way that their work can be viewed as an extension of Siebenmann's dissertation that can be applied to manifolds with non-stable fundamental group at infinity, our main theorem can also be viewed as an extension of the recent Gu-Guilbault characterization of completable $n$-manifolds in a manner that is applicable to manifolds whose fundamental group at infinity is not peripherally stable.