07-1352/Class Notes for March 20

07-1352/Navigation Panel   Back to 06-1350 # Week of... Links 1 Jan 9 About, Notes 2 Jan 16 Notes 3 Jan 23 Notes 4 Jan 30 Notes and Plans 5 Feb 6 Notes 6 Feb 13 Notes R Feb 20 Reading week 7 Feb 27 Notes 8 Mar 6 Notes 9 Mar 13 Notes 10 Mar 20 Notes 11 Mar 27 Notes 12 Apr 3 Map 13 Apr 10 Dancso SP Apr 17 Chu, Sankaran, Amir-Khosravi Suggested Student Topics

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

• Uniqueness up to vertex operations, vaguely.
• The group [math]\displaystyle{ {\mathcal A}^V\subset {\mathcal A}(\theta) }[/math] and its action on the set [math]\displaystyle{ {\mathcal Z} }[/math] of [math]\displaystyle{ {\mathcal A} }[/math]-valued algebraic knot theories.
• An aside about trinions (also see 06-1350/Class Notes for Tuesday October 10).
• The group [math]\displaystyle{ {\mathcal A}^F\subset {\mathcal A}(\uparrow_2) }[/math] and its action on the set of all associators.
• An aside about braided [math]\displaystyle{ \theta }[/math]-graphs:

(Also see 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.