Date of Graduation

8-2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor

Yo'av Rieck

Committee Member

Chaim Goodman-Strauss

Second Committee Member

Mark E. Arnold

Keywords

Pure sciences; Applied sciences; Automorphism groups; Graph groups; Partially commutative groups; Polynomial time; Right-angled artin groups; Word problems

Abstract

We provide an algorithm which takes any given automorphism f of any given right-angled Artin group G and determines whether or not f is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given right-angled Artin group.

Share

COinS