Diagram Genus, Generators, and Applications

Alexander Stoimenow

ISBN 10: 1498733808 / ISBN 13: 9781498733809

Editore: Taylor & Francis Ltd (Sales) Feb 2016, 2016

Riguardo questo articolo

Neuware - 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.

Codice articolo 9781498733809

Dati bibliografici

• Titolo: Diagram Genus, Generators, and Applications
• Editore: Taylor & Francis Ltd (Sales) Feb 2016
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 1498733808
• ISBN 13: 9781498733809
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 231 L x 155 A x 15 P (millimetri) 231 millimetri di larghezza per 155 millimetri di altezza per 15 millimetri di profondità
• Peso: 386 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Alexander Stoimenow is an assistant professor in the GIST College at the Gwangju Institute of Science and Technology. He was previously an assistant professor in the Department of Mathematics at Keimyung University, Daegu, South Korea. His research covers several areas of knot theory, with relations to combinatorics, number theory, and algebra. He earned a PhD from the Free University of Berlin.