Vassily Olegovich Manturov (Russia Moscow State University)

Knot Theory

Second Edition

• Broschiertes Buch

Produktbeschreibung

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 invariant

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Produktdetails

• Verlag: Taylor & Francis Ltd
• 2 ed
• Seitenzahl: 580
• Erscheinungstermin: 30. September 2020
• Englisch
• Abmessung: 234mm x 156mm x 31mm
• Gewicht: 870g
• ISBN-13: 9780367657291
• ISBN-10: 0367657295
• Artikelnr.: 59994695

Autorenporträt

Vassily Olegovich Manturov is professor of Geometry and Topology at Bauman Moscow State Technical University.

Inhaltsangabe

Knots, links, and invariant polynomials. Introduction. Reidemeister moves.
Knot arithmetics. Links in 2-surfaces in R3.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.
Theory of braids. Braids, links and representations of braid groups. Braids
and links. Braid construction algorithms. Algorithms of braid recognition.
Markov's theorem; the Yang-Baxter equation. Vassiliev's invariants.
Definition and Basic notions of Vassiliev invariant theory. The chord
diagram algebra. The Kontsevich integral and formulae for the Vassiliev
invariants. Atoms and d-diagrams. Atoms, height atoms and knots. The
bracket semigroup of knots. Virtual knots. Basic definitions and
motivation. Invariant polynomials of virtual links. Generalised
Jones-Kauffman polynomial. Long virtual knots and their invariants. Virtual
braids. Other theories. 3-manifolds and knots in 3-manifolds. Legendrian
knots and their invariants. Independence of Reidemeister moves.