Combinatorial Knot Theory

Roger A Fenn (Autor)

Buch | Hardcover

208 Seiten

2024
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-12-9272-9 (ISBN)

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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.

Erscheinungsdatum	11.12.2024
Reihe/Serie	Series on Knots & Everything ; 76
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	981-12-9272-8 / 9811292728
ISBN-13	978-981-12-9272-9 / 9789811292729
Zustand	Neuware