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Properties of Closed 3-Braids and Braid Representations of Links

  • Book
  • © 2017

Overview

Authors:
  1. Alexander Stoimenow

    1. School of General Studies, Gwangju Institute of Science and Technology, Gwangju, Korea (Republic of)

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Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Alexander Stoimenow
    Pages 1-4

  3. Preliminaries, Basic Definitions, and Conventions

    • Alexander Stoimenow
    Pages 5-14

  4. Xu’s Form and Seifert Surfaces

    • Alexander Stoimenow
    Pages 15-21

  5. Polynomial Invariants

    • Alexander Stoimenow
    Pages 23-38

  6. Positivity of 3-Braid Links

    • Alexander Stoimenow
    Pages 39-55

  7. Studying Alternating Links by Braid Index

    • Alexander Stoimenow
    Pages 57-62

  8. Applications of the Representation Theory

    • Alexander Stoimenow
    Pages 63-92

  9. Back Matter

    Pages 93-110
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Keywords

About this book

This book studies diverse aspects of braid representations via knots and links. Complete classification results are illustrated for several properties through Xu’s normal 3-braid form and the Hecke algebra representation theory of link polynomials developed by Jones. Topological link types are identified within closures of 3-braids which have a given Alexander or Jones polynomial. Further classifications of knots and links arising by the closure of 3-braids are given, and new results about 4-braids are part of the work. Written with knot theorists, topologists,and graduate students in mind, this book features the identification and analysis of effective techniques for diagrammatic examples with unexpected properties.

Reviews

“This book contains various interesting and detailed properties of polynomial invariants of closed 3-braids (or 4-braids). This makes a nice complement to a survey by J. S. Birman and W. W. Menasco … where properties of closed 3-braids, mainly focused on the classification theorem, are summarized.” (Tetsuya Ito, Mathematical Reviews, August, 2018)​

Authors and Affiliations

  • School of General Studies, Gwangju Institute of Science and Technology, Gwangju, Korea (Republic of)

    Alexander Stoimenow

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