Quandles: An Introduction to the Algebra of Knots
About this Title
Mohamed Elhamdadi, University of South Florida, Tampa, FL and Sam Nelson, Claremont McKenna College, Claremont, CA
Publication: The Student Mathematical Library
Publication Year 2015: Volume 74
ISBNs: 978-1-4704-2213-4 (print); 978-1-4704-2572-2 (online)
MathSciNet review: MR3379534
MSC: Primary 57M27; Secondary 20F99, 57M25
From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and professionals alike. Quandles are essentially knots translated into algebra.
This book provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. With elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more, this book is perfect for a transition course, an upper-division mathematics elective, preparation for research in knot theory, and any reader interested in knots.
Undergraduate and graduate students and research mathematicians interested in low-dimensional topology, in particular, knot theory.
Table of Contents
- Chapter 1. Knots and links
- Chapter 2. Algebraic structures
- Chapter 3. Quandles
- Chapter 4. Quandles and groups
- Chapter 5. Generalizations of quandles
- Chapter 6. Enhancements
- Chapter 7. Generalized knots and links