On the automaticity of the outer automorphism groups of right-angled Coxeter groups

Author

Cameron Haas

Date of Award

2018

First Advisor

Timothy Susse

Second Advisor

William Dunbar

Abstract

We consider the automaticity of the outer automorhism groups of right-angled Coxeter groups. We begin by introducing geometric group theory topics including presentations, Cayley graphs, Coxeter groups and their automorphisms, and automatic structures for a general audience. Afterwards, we include necessary information about automa and group theory before a survey of group presentations, the word metric, quasi-isometry, automaticity, and rewriting systems. Our final section of review focuses upon Coxeter groups and their automorphisms, defining right-angled Coxeter groups as the graph products with vertex groups isomorphic to Z₂. We justify our focus on outer automorphims by noting how they map re ections of the Davis complex to re ections of the Davis complex and summarize past results on the outer automorphisms of right-angled Coxeter groups. Contingent upon a specific conjecture, we answer `is Out⁰(W(Γ₄)) automatic' affirmatively.

Recommended Citation

Haas, Cameron, "On the automaticity of the outer automorphism groups of right-angled Coxeter groups" (2018). Senior Theses. 1214.
https://digitalcommons.bard.edu/sr-theses/1214