Date of Award

August 2023

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Craig Guilbault

Committee Members

Jonah Gaster, Christopher Hruska, Boris Okun, Jeb Willenbring

Keywords

Boundaries, Collapsibility, Topology, Z-sets

Abstract

We extend the notion of collapsibility to non-compact complexes and prove collapsibility of locally-finite CAT(0) cube complexes. Namely, we construct such a cube complex $X$ out of nested convex compact subcomplexes $\{C_i\}_{i=0}^\infty$ with the properties that $X=\cup_{i=0}^\infty C_i$ and $C_i$ collapses to $C_{i-1}$ for all $i\ge 1$.

We then define bonding maps $r_i$ between the compacta $C_i$ and construct an inverse sequence yielding the inverse limit space $\varprojlim\{C_i,r_i\}$. This will provide a new way of Z-compactifying $X$. In particular, the process will yield a new Z-boundary, called the cubical boundary.

Included in

Mathematics Commons

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