Properties of Closed 3-Braids and Braid Representations of Links

ISBN-13: 9783319681481 / Angielski / Miękka / 2017 / 110 str.

Alexander Stoimenow

Opis

This book studies diverse aspects of braid representations via knots and links. 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.

Recenzje

"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)

Spis treści

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.