LEADER 00000cam a2200781Ka 4500 
001    ocn795705254 
003    OCoLC 
005    20190405013545.7 
006    m     o  d         
007    cr cnu---unuuu 
008    120618s2012    nyu     ob    001 0 eng d 
019    817936442 
020    9781139424097|q(electronic book) 
020    1139424092|q(electronic book) 
020    9781139107846|q(electronic book) 
020    1139107844|q(electronic book) 
020    9781139422055 
020    1139422057 
020    1139420003 
020    9781139420006 
020    1280685190 
020    9781280685194 
020    |z9781107020832 
020    |z1107020832 
024 8  9786613662132 
035    (OCoLC)795705254|z(OCoLC)817936442 
037    366213|bMIL 
040    N$T|beng|epn|cN$T|dCOO|dYDXCP|dOCLCQ|dCAMBR|dOCLCQ|dOCLCF
       |dNLGGC|dOCLCQ|dHEBIS|dOCLCO|dNRC|dUAB|dOCLCQ 
049    RIDW 
050  4 QA612.2|b.C48 2012eb 
072  7 MAT|x038000|2bisacsh 
072  7 PBM|2bicssc 
082 04 514/.2242|223 
084    MAT038000|2bisacsh 
090    QA612.2|b.C48 2012eb 
100 1  Chmutov, S.|q(Sergei),|d1959-|0https://id.loc.gov/
       authorities/names/n2012027015 
245 10 Introduction to Vassiliev knot invariants /|cS. Chmutov, 
       S. Duzhin, J. Mostovoy. 
264  1 New York :|bCambridge University Press,|c2012. 
300    1 online resource 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
340    |gpolychrome|2rdacc 
347    text file|2rdaft 
504    Includes bibliographical references and index. 
505 0  Cover; INTRODUCTION TO VASSILIEV KNOT INVARIANTS; Title; 
       Copyright; Dedication; Contents; Preface; 1 Knots and 
       their relatives; 1.1 Definitions and examples; 1.2 Plane 
       knot diagrams; 1.3 Inverses and mirror images; 1.4 Knot 
       tables; 1.5 Algebra of knots; 1.6 Tangles, string links 
       and braids; 1.7 Variations; Exercises; 2 Knot invariants; 
       2.1 Definition and first examples; 2.2 Linking number; 2.3
       The Conway polynomial; 2.4 The Jones polynomial; 2.5 
       Algebra of knot invariants; 2.6 Quantum invariants; 2.7 
       Two-variable link polynomials; Exercises; 3 Finite type 
       invariants. 
505 8  3.1 Definition of Vassiliev invariants3.2 Algebra of 
       Vassiliev invariants; 3.3 Vassiliev invariants of degrees 
       0, 1 and 2; 3.4 Chord diagrams; 3.5 Invariants of framed 
       knots; 3.6 Classical knot polynomials as Vassiliev 
       invariants; 3.7 Actuality tables; 3.8 Vassiliev invariants
       of tangles; Exercises; 4 Chord diagrams; 4.1 Four- and one
       -term relations; 4.2 The Fundamental Theorem; 4.3 
       Bialgebras of knots and of Vassiliev knot invariants; 4.4 
       Bialgebra of chord diagrams; 4.5 Bialgebra of weight 
       systems; 4.6 Primitive elements in A; 4.7 Linear chord 
       diagrams; 4.8 Intersection graphs; Exercises. 
505 8  5 Jacobi diagrams5.1 Closed Jacobi diagrams; 5.2 IHX and 
       AS relations; 5.3 Isomorphism A?C; 5.4 Product and 
       coproduct in C; 5.5 Primitive subspace of C; 5.6 Open 
       Jacobi diagrams; 5.7 Linear isomorphism B?C; 5.8 More on 
       the relation between B and C; 5.9 The three algebras in 
       small degrees; 5.10 Jacobi diagrams for tangles; 5.11 
       Horizontal chord diagrams; Exercises; 6 Lie algebra weight
       systems; 6.1 Lie algebra weight systems for the algebra A;
       6.2 Lie algebra weight systems for the algebra C; 6.3 Lie 
       algebra weight systems for the algebra B; 6.4 Lie 
       superalgebra weight systems; Exercises. 
505 8  7 Algebra of 3-graphs7.1 The space of 3-graphs; 7.2 Edge 
       multiplication; 7.3 Vertex multiplication; 7.4 Action of? 
       on the primitive space P; 7.5 Lie algebra weight systems 
       for the algebra?; 7.6 Vogel's algebra?; Exercises; 8 The 
       Kontsevich integral; 8.1 First examples; 8.2 The 
       construction; 8.3 Example of calculation; 8.4 The 
       Kontsevich integral for tangles; 8.5 Convergence of the 
       integral; 8.6 Invariance of the integral; 8.7 Changing the
       number of critical points; 8.8 The universal Vassiliev 
       invariant; 8.9 Symmetries and the group-like property of 
       Z(K). 
505 8  8.10 Towards the combinatorial Kontsevich 
       integralExercises; 9 Framed knots and cabling operations; 
       9.1 Framed version of the Kontsevich integral; 9.2 Cabling
       operations; 9.3 Cabling operations and the Kontsevich 
       integral; 9.4 Cablings of the Lie algebra weight systems; 
       Exercises; 10 The Drinfeld associator; 10.1 The KZ 
       equation and iterated integrals; 10.2 Calculation of the 
       KZ Drinfeld associator; 10.3 Combinatorial construction of
       the Kontsevich integral; 10.4 General associators; 
       Exercises; 11 The Kontsevich integral: advanced features; 
       11.1 Mutation; 11.2 Canonical Vassiliev invariants. 
520    "With hundreds of worked examples, exercises and 
       illustrations, this detailed exposition of the theory of 
       Vassiliev knot invariants opens the field to students with
       little or no knowledge in this area. It also serves as a 
       guide to more advanced material. The book begins with a 
       basic and informal introduction to knot theory, giving 
       many examples of knot invariants before the class of 
       Vassiliev invariants is introduced. This is followed by a 
       detailed study of the algebras of Jacobi diagrams and 3-
       graphs, and the construction of functions on these 
       algebras via Lie algebras. The authors then describe two 
       constructions of a universal invariant with values in the 
       algebra of Jacobi diagrams: via iterated integrals and via
       the Drinfeld associator, and extend the theory to framed 
       knots"--|cProvided by publisher. 
588 0  Print version record. 
590    eBooks on EBSCOhost|bEBSCO eBook Subscription Academic 
       Collection - North America 
650  0 Knot theory.|0https://id.loc.gov/authorities/subjects/
       sh85072726 
650  0 Invariants.|0https://id.loc.gov/authorities/subjects/
       sh85067665 
650  7 Knot theory.|2fast|0https://id.worldcat.org/fast/988171 
650  7 Invariants.|2fast|0https://id.worldcat.org/fast/977982 
655  4 Electronic books. 
700 1  Duzhin, S. V.|q(Sergeĭ Vasilʹevich),|d1956-|0https://
       id.loc.gov/authorities/names/n2004007121 
700 1  Mostovoy, J.|q(Jacob)|0https://id.loc.gov/authorities/
       names/n2012027019 
776 08 |iPrint version:|aChmutov, S. (Sergei), 1959-
       |tIntroduction to Vassiliev knot invariants.|dNew York : 
       Cambridge University Press, 2012|z9781107020832|w(DLC)  
       2012010339|w(OCoLC)758397428 
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
       search.ebscohost.com/login.aspx?direct=true&scope=site&
       db=nlebk&AN=451648|zOnline eBook via EBSCO. Access 
       restricted to current Rider University students, faculty, 
       and staff. 
856 42 |3Instructions for reading/downloading the EBSCO version 
       of this eBook|uhttp://guides.rider.edu/ebooks/ebsco 
901    MARCIVE 20231220 
948    |d20190507|cEBSCO|tEBSCOebooksacademic NEW 4-5-19 7552
       |lridw 
994    92|bRID