© 2017

Properties of Closed 3-Braids and Braid Representations of Links


Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Alexander Stoimenow
    Pages 1-4
  3. Alexander Stoimenow
    Pages 5-14
  4. Alexander Stoimenow
    Pages 15-21
  5. Alexander Stoimenow
    Pages 23-38
  6. Alexander Stoimenow
    Pages 39-55
  7. Alexander Stoimenow
    Pages 57-62
  8. Alexander Stoimenow
    Pages 63-92
  9. Back Matter
    Pages 93-110

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.


link polynomial positive braid strongly quasi-positive link Positivity of 3-braid links Seifert surface Burau representation incompressible surface Seifert surfaces Morton-Franks-Williams bound Applications of representation theory Recovering the Burau trace Mahler measures Fibered Dean knots Alexander polynomial Jones polynomial Gauß sum invariants

Authors and affiliations

  1. 1.School of General StudiesGwangju Institute of Science and TechnologyGwangjuKorea (Republic of)

Bibliographic information


“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)​