07-1352/Class Notes for March 20: Difference between revisions

Revision as of 10:58, 20 March 2007

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

Uniqueness up to vertex operations, vaguely.
The group ${\mathcal {A}}^{V}\subset {\mathcal {A}}(\theta )$ and its action on the set ${\mathcal {Z}}$ of ${\mathcal {A}}$ -valued algebraic knot theories.
A word about trinions (also see 06-1350/Class Notes for Tuesday October 10).
The group ${\mathcal {A}}^{F}\subset {\mathcal {A}}(\uparrow _{2})$ and its action on the set of all associators.
A word about braided $\theta$ -graphs:

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 {{07-1352/Navigation}}
-{{In Preparation}}
+'''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.
+* A word 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.
+* A word 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.