An Invitation to Knot Theory: Virtual and Classical

✍ Scribed by Heather A. Dye

• Publisher: CRC Press;Chapman and Hall/CRC
• Year: 2016
• Tongue: English
• Leaves: 284
• Edition: 1
• Category: Library

✦ Synopsis

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory

An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra.

The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.

✦ Table of Contents

Content: Front Cover
Dedication
Contents
List of Figures
List of Tables
Preface
Acknowledgments
About the author
Symbol List
Section I --
Knots and crossings
Chapter 1 --
Virtual knots and links
Chapter 2 --
Linking invariants
Chapter 3 --
A multiverse of knots
Chapter 4 --
Crossing invariants
Chapter 5 --
Constructing knots
Section II --
Knot polynomials
Chapter 6 --
The bracket polynomial
Chapter 7 --
Surfaces
Chapter 8 --
Bracket polynomial II
Chapter 9 --
The checkerboard framing
Chapter 10 --
Modifications of the bracket polynomial
Section III --
Algebraic structures Chapter 11 --
QuandlesChapter 12 --
Knots and quandles
Chapter 13 --
Biquandles
Chapter 14 --
Gauss diagrams
Chapter 15 --
Applications
Appendix A --
Tables
Appendix B --
References by chapter
Back Cover

✦ Subjects

Knot theory;MATHEMATICS / Topology