Date of Award

5-1-2021

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (viii, 96 pages) : illustrations (some color)

Dissertation/Thesis Chair

Mattew Zaremsky

Committee Members

Marco Varisco, Alex Tchernev, Boris Goldfarb

Keywords

braided, group, Thompson, Group theory, Braid theory, Trees (Graph theory)

Subject Categories

Physical Sciences and Mathematics

Abstract

We construct braided versions of the Brin-Thompson groups and prove that they are of type F infinity. The proof involves showing that the matching complexes of colored arcs on surfaces are highly connected. In order to do so we develop the tools and definitions from algebraic topology and group theory, including results about some other Thompson-like groups. The main result, and the thesis as a whole, provides an infinite family of braided relatives of Thompson groups that are all of type F infinity.

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