Diagram Genus, Generators, and Applications

By Alexander Stoimenow

In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). This book 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. He gives a detailed structure theorem for canonical Seifert surfaces of a given genus and covers applications, such as the braid index of alternating knots and hyperbolic volume.

• Format: Hardcover
• Language: English
• ISBN: 1498733808
• ISBN13: 9781498733809
• Release Date: February 2016
• Publisher: CRC Press
• Length: 174 Pages
• Weight: 0.85 lbs.
• Dimensions: 0.6" x 6.1" x 9.1"