Kazhdan's Seminar on Khovanov Theory: Winter 2005

Sunday 4-6 in Maths Bldg 209

Outline of possible topics:
  1. What is knot theory? Kauffman bracket construction of Jones polynomial of knots in a 3-sphere.
  2. Witten's generalisation of Jones polynomial to the case of knots in an arbitrary 3-manifold and the Reshetikhin-Turaev construction of Witten's invariants. Background on U_qsl_2 and its representation theory.
  3. Topological quantum field theories, the 2-dimensional case [Frobenius algebras] and Reshetikhin-Turaev's example of a 3-dimensional Topological Quantum Field Theory.
  4. Definition of Khovanov homology theories for links induced by Frobenius systems (a la Khovanov).
  5. Universal Bar-Natan morphism between planar algebras of tangle diagrams and of complexes of cobordisms.
  6. Homotopy of complexes and reduction to Bar-Natan morphism from planar algebra of tangles to planar algebra of complexes up to homotopy type, to cobordisms up to cobordism relations.
  7. Beginnings of categorification of 3-manifold invariant (equivalent to 4-TQFT) in math.QA/0509083 "Hopfological algebra and categorifications at a root of unity".

Sources for topics (participants should choose a topic and lecture on it!)
Seminars given

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Last modified January 25th, 2001.
Comments and questions to ruthel@ma.huji.ac.il