Combinatorial Knot Theory

Roger A Fenn (University Of Sussex, Uk)

$180.95 $144.48

Hardback

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English

World Scientific Publishing Co Pte Ltd
10 January 2025

Topology; Combinatorics & graph theory

Series: Series on Knots & Everything

Summary
Details

A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or network in the horizontal plane, with the vertices or crossings corresponding to double points of a projection. At this stage we have the shadow of the knot defined by the projection. We can reconstruct the knot by lifting the crossings into two points in space, one above the other. This information is preserved at the vertices by cutting the arc which appears to go under the over crossing arc. We can then act on this diagram of the knot using the famous Reidemeister moves to mimic the motion of the knot in space. The result is classic combinatorial knot theory. In recent years, many different types of knot theories have been considered where the information stored at the crossings determines how the Reidemeister moves are used, if at all.

In this book, we look at all these new theories systematically in a way which any third-year undergraduate mathematics student would understand. This book can form the basis of an undergraduate course or as an entry point for a postgraduate studying topology.

By: Roger A Fenn (University Of Sussex Uk)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Volume: 76
ISBN: 9789811292729
ISBN 10: 9811292728
Series: Series on Knots & Everything
Pages: 208
Publication Date: 10 January 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

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Combinatorial Knot Theory

Roger A Fenn (University Of Sussex, Uk)

$180.95 $144.48

Hardback

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