000			02646nam a22003618i 4500
001			CR9781139107846
003			UkCbUP
005			20200124160256.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110708s2012||||enk o ||1 0|eng|d
020			_a9781139107846 (ebook)
020			_z9781107020832 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA612.2 _b.C48 2012
082	0	0	_a514/.2242 _223
100	1		_aChmutov, S. _q(Sergei), _d1959- _eauthor.
245	1	0	_aIntroduction to Vassiliev knot invariants / _cS. Chmutov, S. Duzhin, J. Mostovoy.
264		1	_aCambridge : _bCambridge University Press, _c2012.
300			_a1 online resource (xvi, 504 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	8		_aMachine generated contents note: 1. Knots and their relatives; 2. Knot invariants; 3. Finite type invariants; 4. Chord diagrams; 5. Jacobi diagrams; 6. Lie algebra weight systems; 7. Algebra of 3-graphs; 8. The Kontsevich integral; 9. Framed knots and cabling operations; 10. The Drinfeld associator; 11. The Kontsevich integral: advanced features; 12. Braids and string links; 13. Gauss diagrams; 14. Miscellany; 15. The space of all knots; Appendix; References; Notations; Index.
520			_aWith 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. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.
650		0	_aKnot theory.
650		0	_aInvariants.
700	1		_aDuzhin, S. V. _q(Sergeĭ Vasilʹevich), _d1956- _eauthor.
700	1		_aMostovoy, J. _q(Jacob), _eauthor.
776	0	8	_iPrint version: _z9781107020832
856	4	0	_uhttps://doi.org/10.1017/CBO9781139107846
999			_c519925 _d519923