Properties of Closed 3-Braids and Braid Representations of Links , 1st ed. 2017 SpringerBriefs in Mathematics Series
Auteur : Stoimenow Alexander
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.
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.
Includes supplementary material: sn.pub/extras
Date de parution : 12-2017
Ouvrage de 110 p.
15.5x23.5 cm
Mots-clés :
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
