Articoli correlati a Virtual Knots: The State of the Art: 51

Virtual Knots: The State of the Art: 51 - Rilegato

Manturov, Vassily Olegovich; Ilyutko, Denis Petrovich

 
9789814401128: Virtual Knots: The State of the Art: 51
Rilegato
ISBN 10: 9814401129 ISBN 13: 9789814401128
Casa editrice: World Scientific Pub Co Inc, 2012

Sinossi

The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as “diagramless knot theory”: such “links” have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.

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Editore
World Scientific Pub Co Inc
Data di pubblicazione
2012
Lingua
Inglese
ISBN 10 
9814401129
ISBN 13 
9789814401128
Rilegatura
Copertina rigida
Numero di pagine
521
Contatto del produttore
non disponibile
Persona responsabile
gpsr@libri.de
gpsr@libri.de

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