Diagram Genus, Generators, and Applications (Hardcover)

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.

General

Imprint:	Productivity Press
Country of origin:	United States
Series:	Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Release date:	February 2016
First published:	2016
Authors:	Alexander Stoimenow
Dimensions:	235 x 156 x 15mm (L x W x T)
Format:	Hardcover
Pages:	174
ISBN-13:	978-1-4987-3380-9
Categories:	Books > Science & Mathematics > Mathematics > Combinatorics & graph theory Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Geometry > General Books > Science & Mathematics > Mathematics > Topology > Algebraic topology Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	1-4987-3380-8
Barcode:	9781498733809

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