Hyperbolic Knot Theory by Jessica S Purcell

Hyperbolic Knot Theory by Jessica S Purcell

This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.

Jessica S. Purcell, Monash University, Clayton, Victoria, Australia

SKU	Nicht verfügbar
ISBN 13	9781470454999
ISBN 10	1470454998
Titel	Hyperbolic Knot Theory
Autor	Jessica S Purcell
Serie	Graduate Studies In Mathematics
Buchzustand	Nicht verfügbar
Bindungsart	Paperback
Verlag	American Mathematical Society
Erscheinungsjahr	2021-01-30
Seitenanzahl	369
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar