Knot at Lunch, May 24, 2007

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First meeting for summer 2007! Peter Lee is telling us about associators with frozen feet. See also his handout from the CMS Winter 2006 Session on Knot Homologies - front: CMS 2006 Lee Handout Front.png, back: CMS 2006 Lee Handout Back.png and Dror's very partial paperlet, Associators with Frozen Feet.

  • Definition of and its relation with finite type invariants.
  • The frozen feet quotient.
  • The action of , , and of , etc. (Dror: see also VS, TS and TG Algebras.)
  • Generators and relations: , , the hexagons and pentagon, unitarity, non-degeneracy, group-like property.
  • if and similar identities.
  • , and in our case, this is just !
  • .
  • . With this, we have as follows:
  • Unitarity becomes .
  • where .
  • Likewise for all other terms in the hexagon, which becomes
  • Simplifying using frozen feet, this becomes
  • Alternatively,