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Title Knot theory / by Vassily Manturov.
Imprint Boca Raton, FL : CRC Press, [2018]


 Internet  Electronic Book    AVAILABLE
Edition Second edition.
Description 1 online resource (xix, 559 pages) : illustrations
Note "A Chapman & Hall book."
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
Description based on print version record.
Subject Knot theory.
Genre Electronic books.
Contents Introduction -- Reidemeister moves. Knot arithmetics -- Links in 2-surfaces in R3. Simplest link invariants -- Fundamental group. The knot group -- The knot quandle and the Conway algebra -- Kauffman's approach to Jones polynomial -- Properties of Jones polynomials. Khovanov's complex -- Lee-Rasmussen invariant, slice knots, and the genus conjecture -- Braids, links and representations of braid groups -- Braids and links. Braid construction algorithms -- Algorithms of braid recognition -- Markov's theorem. The Yang Baxter equation -- Definitions and basic notions of Vassiliev invariant theory -- The chord diagram algebra -- The Kontsevich integral and formulae for the Vassiliev invariants -- Atoms, height atoms and knots -- Virtual knots. Basic definitions and motivation -- Invariant polynomials of virtual links -- Generalised Jones-Kauffman polynomial -- Long virtual knots and their invariants -- Virtual braids -- Khovanov homology of virtual knots -- 3-manifolds and knots in 3-manifolds -- Heegaard-Floer homology -- Legendrian knots and their invariants.
Summary Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and algebra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a professional reference and will serve equally well as a text for a course on knot theory.
Other Title Print version: Manturov, V. O. (Vasiliĭ Olegovich). Knot theory. Second edition. Boca Raton, Florida : CRC Press, Taylor & Francis Group, [2018] 9781138561243