A01=Denis Petrovich Ilyutko
A01=Vassily Olegovich Manturov
Atom
Author_Denis Petrovich Ilyutko
Author_Vassily Olegovich Manturov
Braid
Category=PBP
Cobordism
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Finite-Type Invariant
Graph-Link
Jones Polynomial
Kauffman Bracket
Khovanov Homology
Knot
Kuperberg Theorem
Link
Long Knot
Parity
Qroupoid
Quandle
Reidemeister Moves
Vassiliev Invariant
Virtual Braid
Virtual Knot
Virtual Link
Product details
- ISBN 9789814401128
- Publication Date: 28 Nov 2012
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
