Virtual knots : the state of the art / Vassily Olegovich Manturov, Denis Petrovich Ilyutko.
"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...
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| Uniform Title: | Virtualʹnye uzly. English |
|---|---|
| Main Author: | |
| Other Authors: | |
| Language: | English |
| Language of the Original: |
Russian |
| Published: |
Hackensack, NJ :
World Scientific,
[2013], ©2013.
|
| Series: | K & E series on knots and everything ;
v. 51. |
| Subjects: | |
| Physical Description: | xxv, 521 pages : illustrations ; 24 cm. |
| Format: | Book |
MARC
| LEADER | 00000cam a22000008a 4500 | ||
|---|---|---|---|
| 001 | in00005099670 | ||
| 003 | OCoLC | ||
| 005 | 20220616052837.0 | ||
| 008 | 120423t20132013njua b 001 0 eng | ||
| 010 | |a 2012010601 | ||
| 020 | |a 9789814401128 | ||
| 020 | |a 9814401129 | ||
| 035 | |a (CaEvSKY)sky254892951 | ||
| 035 | |a (OCoLC)849250169 | ||
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| 100 | 1 | |a Manturov, V. O. |q (Vasiliĭ Olegovich) |0 http://id.loc.gov/authorities/names/n2012027727 |0 http://id.loc.gov/authorities/names/n2003019400 | |
| 240 | 1 | 0 | |a Virtualʹnye uzly. |l English |0 http://id.loc.gov/authorities/names/n2012027727 |
| 245 | 1 | 0 | |a Virtual knots : |b the state of the art / |c Vassily Olegovich Manturov, Denis Petrovich Ilyutko. |
| 260 | |a Hackensack, NJ : |b World Scientific, |c [2013], ©2013. | ||
| 300 | |a xxv, 521 pages : |b illustrations ; |c 24 cm. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on knots and everything ; |v vol. 51 | |
| 504 | |a Includes bibliographical references (pages 499-514) and index. | ||
| 505 | 0 | |a Basic Definitions and Notions -- Virtual Knots and Three-Dimensional Topology -- Quandles (Distributive Groupoids) in Virtual Knot Theory -- The Jones-Kauffman Polynomial: Atoms -- Khovanov Homology -- Virtual Braids -- Vassiliev's Invariants and Framed Graphs -- Parity in Knot Theory: Free-Knots: Cobordisms -- Theory of Graph-Links. | |
| 520 | |a "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."--Publisher's website. | ||
| 650 | 0 | |a Knot theory. |0 http://id.loc.gov/authorities/subjects/sh85072726 | |
| 700 | 1 | |a Ilʹi︠u︡tko, D. P. |q (Denis Petrovich), |d 1979- |0 http://id.loc.gov/authorities/names/n2012026986 | |
| 830 | 0 | |a K & E series on knots and everything ; |v v. 51. |0 http://id.loc.gov/authorities/names/n91052105 | |
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| 952 | f | f | |p Can Circulate |a Michigan State University-Library of Michigan |b Michigan State University |c MSU Main Library |d MSU Main Library |t 0 |e QA612.2 .M36413 2013 |h Library of Congress classification |i Printed Material |m 31293007461332 |n 1 |