thesis_access.pdf (553.81 kB)

Groupoids associated to inverse semigroups

Download (553.81 kB)
thesis
posted on 06.04.2021, 21:47 by Jones, Malcolm

Starting with an arbitrary inverse semigroup with zero, we study two well-known groupoid constructions, yielding groupoids of filters and groupoids of germs. The groupoids are endowed with topologies making them étale. We use the bisections of the étale groupoids to show there is a topological isomorphism between the groupoids. This demonstrates a widely useful equivalence between filters and germs. We use the isomorphism to characterise Exel’s tight groupoid of germs as a groupoid of filters, to find a nice basis for the topology on the groupoid of ultrafilters and to describe the ultrafilters in the inverse semigroup of an arbitrary self-similar group.

History

Advisor 1

Orloff Clark, Lisa

Advisor 2

an Huef, Astrid

Copyright Date

01/04/2021

Date of Award

01/04/2021

Publisher

Victoria University of Wellington - Te Herenga Waka

Rights License

CC BY-ND 4.0

Degree Discipline

Mathematics

Degree Grantor

Victoria University of Wellington - Te Herenga Waka

Degree Level

Masters

Degree Name

Master of Science

ANZSRC Type Of Activity code

1 PURE BASIC RESEARCH

Victoria University of Wellington Item Type

Awarded Research Masters Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics and Statistics

Exports