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Combinatorial Knot Theory

Name: Combinatorial Knot Theory
Brand: World Scientific Publishing Company
SKU: 45748192
Price: 31405 HUF
Availability: InStock
Author: Fenn
ISBN: 9789811292729

Fenn

Roger A (University Of Sussex

Uk)

Language

English

Book Hardback

Libristo code: 45748192

Publishers World Scientific Publishing Company, October 2024

A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent... Full description

Libristo code: 45748192

214 b

31 405 Ft

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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.