Artin groups and local indicability

Artin groups and local indicability

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This thesis consists of two parts. The first part (chapters 1 and 2) consists of an introduction to theory of Coxeter groups and Artin groups. This material, for the most part, has been known for over thirty years, however, we do mention some recent developments where appropriate. In the second part...

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Main Author: Mulholland, Jamie Thomas
Format: Others
Language:English
Published: 2009
Online Access:http://hdl.handle.net/2429/13292
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spelling ndltd-UBC-oai-circle.library.ubc.ca-2429-132922018-01-05T17:36:46Z Artin groups and local indicability Mulholland, Jamie Thomas This thesis consists of two parts. The first part (chapters 1 and 2) consists of an introduction to theory of Coxeter groups and Artin groups. This material, for the most part, has been known for over thirty years, however, we do mention some recent developments where appropriate. In the second part (chapters 3-5) we present some new results concerning Artin groups of finite-type. In particular, we compute presentations for the commutator subgroups of the irreducible finite-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the braid groups. Using these presentations we determine the local indicability of the irreducible finite-type Artin groups (except for F₄ which at this time remains undetermined). We end with a discussion of the current state of the right-orderability of the finite-type Artin groups. Science, Faculty of Mathematics, Department of Graduate 2009-09-28T23:05:06Z 2009-09-28T23:05:06Z 2002 2002-11 Text Thesis/Dissertation http://hdl.handle.net/2429/13292 eng For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. 3729556 bytes application/pdf
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language English
format Others
sources NDLTD
description This thesis consists of two parts. The first part (chapters 1 and 2) consists of an introduction to theory of Coxeter groups and Artin groups. This material, for the most part, has been known for over thirty years, however, we do mention some recent developments where appropriate. In the second part (chapters 3-5) we present some new results concerning Artin groups of finite-type. In particular, we compute presentations for the commutator subgroups of the irreducible finite-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the braid groups. Using these presentations we determine the local indicability of the irreducible finite-type Artin groups (except for F₄ which at this time remains undetermined). We end with a discussion of the current state of the right-orderability of the finite-type Artin groups. === Science, Faculty of === Mathematics, Department of === Graduate
author Mulholland, Jamie Thomas
spellingShingle Mulholland, Jamie Thomas
Artin groups and local indicability
author_facet Mulholland, Jamie Thomas
author_sort Mulholland, Jamie Thomas
title Artin groups and local indicability
title_short Artin groups and local indicability
title_full Artin groups and local indicability
title_fullStr Artin groups and local indicability
title_full_unstemmed Artin groups and local indicability
title_sort artin groups and local indicability
publishDate 2009
url http://hdl.handle.net/2429/13292
work_keys_str_mv AT mulhollandjamiethomas artingroupsandlocalindicability
_version_ 1718589327035858944

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