Subject(s) 
Knot theory

Physical Description 
xxv, 521 p. : ill. ; 24 cm 
Note 
Includes bibliographical references (p. 499514) and index 
Contents 
Basic Definitions and Notions  Virtual Knots and ThreeDimensional Topology  Quandles (Distributive Groupoids) in Virtual Knot Theory  The JonesKauffman Polynomial: Atoms  Khovanov Homology  Virtual Braids  Vassiliev's Invariants and Framed Graphs  Parity in Knot Theory: FreeKnots: Cobordisms  Theory of GraphLinks 
Summary 
"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 selfcontained and contains uptodate 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 threemanifold 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 graphlink 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. Graphlinks 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 graphlinks one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory."Publisher's website 
NOTE 
531124 
Series 
Series on knots and everything ; v. 51


K & E series on knots and everything ; v. 51

Alternate Author 
Ilʹi︠u︡tko, D. P. (Denis Petrovich), 1979

