{"product_id":"knot-theory-9780367657291","title":"Knot Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eOver the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eKnot Theory, Second Edition\u003c\/strong\u003e 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 profes-sional reference and will serve equally well as a text for a course on knot theory.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003ePraise for the first edition\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThis book is highly recommended for all students and researchers in knot theory, and to those in the sciences and mathematics who would like to get a flavor of this very active field.”\u003cbr\u003e-\u003cstrong\u003eProfessor Louis H. Kauffman\u003c\/strong\u003e, Department of Mathematics, Statistics and Com-puter Science, University of Illinois at Chicago\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eKnots, 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. \u003cb\u003eTheory of braids. \u003c\/b\u003eBraids, links and representations of braid groups. Braids and links. Braid construction algorithms. Algorithms of braid recognition. Markov's theorem; the Yang-Baxter equation. \u003cb\u003eVassiliev's invariants. Definition and Basic notions of Vassiliev invariant theory. \u003c\/b\u003eThe chord diagram algebra. The Kontsevich integral and formulae for the Vassiliev invariants. \u003cb\u003eAtoms and d-diagrams. \u003c\/b\u003eAtoms, height atoms and knots. The bracket semigroup of knots. \u003cb\u003eVirtual knots. \u003c\/b\u003eBasic definitions and motivation. Invariant polynomials of virtual links. Generalised Jones-Kauffman polynomial. Long virtual knots and their invariants. Virtual braids. \u003cb\u003eOther theories. \u003c\/b\u003e3-manifolds and knots in 3-manifolds. Legendrian knots and their invariants. Independence of Reidemeister moves.\u003c\/p\u003e","brand":"CRC Press","offers":[{"title":"Default Title","offer_id":53733837668695,"sku":"9780367657291","price":47.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367657291.jpg?v=1782118858","url":"https:\/\/bookcurl.com\/products\/knot-theory-9780367657291","provider":"Book Curl","version":"1.0","type":"link"}