Alexander Stoimenow

Diagram Genus, Generators, and Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 192
• Erscheinungstermin: 3. September 2018
• Englisch
• ISBN-13: 9781315362199
• Artikelnr.: 54535759

Autorenporträt

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.

Inhaltsangabe

Introduction. Preliminaries. The Maximal Number of Generator Crossings and
~-Equivalance Classes. Generators of Genus 4. Unknot Diagrams, Non-Trivial
Polynomials, and Achiral Knots. The Signature. Braid Index of Alternating
Knots. Minimal String Bennequin Surfaces. The Alexander Polynomial of
Alternating Knots. Outlook.