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Title: Dots and lines : geometric semigroup theory and finite presentability
Author: Awang, Jennifer S.
ISNI:       0000 0004 5364 9786
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 2015
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Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasi-isometry of Cayley graphs. We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup. We show that finite presentability of certain types of direct products, completely (0-)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the Švarc-Milnor Lemma. We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasi-isometry of Cayley graphs for semigroups. We give several skeletons and describe fully the semigroups that can be associated to these.
Supervisor: Ruškuc, Nik; Quick, Martyn Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Semigroups ; Cayley graph ; Finite presentability ; QA183.A8 ; Geometric group theory ; Representations of semigroups ; Cayley graphs