Properties of Closed 3-Braids and Braid Representations of Links / by Alexander Stoimenow.

Format:

Book

Author/Creator:

Stoimenow, Alexander., Author.

Series:

SpringerBriefs in Mathematics, 2191-8201

Language:

English

Subjects (All):

Topological groups.

Lie groups.

Topology.

Group theory.

Functions of complex variables.

Topological Groups and Lie Groups.

Group Theory and Generalizations.

Several Complex Variables and Analytic Spaces.

Local Subjects:

Topological Groups and Lie Groups.

Topology.

Group Theory and Generalizations.

Several Complex Variables and Analytic Spaces.

Physical Description:

1 online resource (X, 110 p. 89 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

1. Introduction

2. Preliminaries, basic definitions and conventions

3. Xu’s form and Seifert surfaces

4. Polynomial invariants

5. Positivity of 3-braid links

6. Studying alternating links by braid index

7. Applications of the representation theory

Appendix. –References.-Index.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-68149-4