View source for 07-1352/Class Notes for March 20

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'''Today's Agenda.''' The up-to-vertex-operations uniqueness of an <math>{\mathcal A}</math>-valued algebraic knot theory.

* Uniqueness up to vertex operations, vaguely.
* The group <math>{\mathcal A}^V\subset {\mathcal A}(\theta)</math> and its action on the set <math>{\mathcal Z}</math> of <math>{\mathcal A}</math>-valued algebraic knot theories.
* An aside about trinions (also see [[06-1350/Class Notes for Tuesday October 10]]).
* The group <math>{\mathcal A}^F\subset {\mathcal A}(\uparrow_2)</math> and its action on the set of all associators.
* An aside about braided <math>\theta</math>-graphs:
[[Image:07-1352 A Braided Theta Graph.png|480px|center]]
:(Also see [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/BraidedThetas/index.html Dror Bar-Natan's Image Gallery: Knotted Objects: Braided Thetas].)
* A degree-by-degree construction of a twistor F and the reduction to homology.
* Computing the homology using unitrivalent graphs and black boxes.
* Return to the PBW theorem.