Artin Groups of Extra-Large Type Are Biautomatic
In this thesis we develop new techniques to work with small cancellation theory diagrams for Artin groups. Using these techniques we examine paths in the Cayley graph of the Artin group. For any Artin group G, with semigroup generators ${\cal A}$, we define a language $L(G) \subset {\cal A}\sp*$. The language L(G) is a set of canonical forms for the Artin group. In the case G is an Artin group of extra-large type or a two generator Artin group, we analyze the geometry of the small cancellation theory diagrams and show that L(G) is the language of a biautomatic structure for G.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign