More Examples of Pseudo-Collars on High-Dimensional Manifolds

TL;DR

This paper generalizes the construction of pseudo-collars on high-dimensional manifolds, moving from specific Thompson's group-based examples to broader classes involving hyperbolic 3-manifold groups.

Contribution

It introduces a more general method for constructing pseudo-collars using fundamental groups of hyperbolic 3-manifolds, expanding previous techniques beyond Thompson's group V.

Findings

Constructed uncountably many pseudo-collars with the same boundary

Extended techniques to broader classes of groups

Demonstrated applications to hyperbolic 3-manifold groups

Abstract

In a previous paper, we developed general techniques for constructing a variety of pseudo-collars, as defined by Guilbault and Tinsley, with roots in earlier work by Chapman and Siebenmann. As an application of our techniques, we exhibited an uncountable collection of pseudo-collars, all with the same boundary and similar fundamental group systems at infinity. Construction of that family was very specific; it relied on properties of Thompson's group $V$. In this paper, we provide a more general approach to constructing similar collections of examples. Instead of using Thompson's group $V$, we base our new examples on a broader and more common collection of groups, in particular, fundamental groups of certain hyperbolic 3-manifolds.