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Title of Thesis

Combinatorial Group Theory of Braid Groups

Author(s)

Usman Ali

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2009
Subject
Mathematics
Number of Pages
66
Keywords (Extracted from title, table of contents and abstract of thesis)
Combinatorial, Group, Theory, Braid, Groups, monoids,  Coxeter groups, conjugacy, Fragments, Garside

Abstract
No Abstract

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

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2

1

PRELIMINARIES

1.1 Braid groups and monoids

1.2 Garside braid and its properties
1.3 Word and conjugacy problem
1.4 Coxeter groups and Artin groups

1.5 Complete presentation of braid monoids

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3 2 RELATIVE GARSIDE ELEMENTS AND COMPLETE PRESENTATION OF SOME ARTIN MONOIDS

2.1 Introduction

2.2 Relative Garside elements

2.3 Fragments of relative Garside elements

2.4 Complete Presentation of Some Artin Monoids

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4 3 CONJUGACY CLASSES OF 3-BRAID GROUP

3.1 Introduction

3.2 Normal form and summit set
3.3 Knots of braid index less or equal three

3.4 Hilbert series of conjugacy classes

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5 4 COMPLETE PRESENTATION AND LEFT-CANONICAL FORM

4.1 Introduction

4.2 Divisors of ón+1
4.3 Computing the exponents
4.4 Left-canonical form

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6 5 BIBLIOGRAPHY

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