In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns (?generators?). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.
Diagram Genus, Generators, and Applications Ebook
By: Alexander Stoimenow
Publisher:
Chapman & Hall
Print ISBN: 9781498733809, 1498733808
eText ISBN: 9781315359984, 1315359987
Edition: 1st
Copyright year: 2016
Format: EPUB
Available from $ 23.18 USD
SKU: 9781315359984R90
Access Full Textbook
? Downloaded copy on your device does not expire..
?
