06-1350/Class Notes for Tuesday November 14

06-1350/Navigation Panel   # Week of... Links 1 Sep 11 About, Tue, Thu 2 Sep 18 Tue, Kurlin(P), Thu 3 Sep 25 Tue, Photo, Thu 4 Oct 2 HW1, Tue, Thu 5 Oct 9 Tue(P), Thu(P) 6 Oct 16 HW2, Tue(P), Thu(P) 7 Oct 23 Tue(P), Thu 8 Oct 30 HW3, Tue, Thu 9 Nov 6 Tue ($\nu$), Thu 10 Nov 13 Tue, Thu 11 Nov 20 HW4(P), Thu 12 Nov 27 Thu 13 Dec 4 Syzygies in Asymptote, Final Jan 8 Grades Note. (P) means "contains a problem that Dror cares about". Add your name / see who's in! On to 07-1352

In Preparation

The information below is preliminary and cannot be trusted! (v)

Today's Agenda

• Recall planar algebras and the planar algebra of shielded chord diagrams.
• Finish describing the necessary relations between $T$, $R$, $\Phi$ and $B^{\pm }$ in verbal form.
• Sweeping clean a tree and ${\mathcal {A}}(\Gamma )\equiv {\mathcal {A}}(\uparrow _{b_{1}(\Gamma )})$.

• ${\mathcal {A}}(\uparrow _{n})$ is a VS-algebra (see more at VS, TS and TG Algebras).
• In the coordinates above, write the $TR\Phi B$ relations in various algebraic notations.
  • R4: $(1230)^{\star }B^{\pm }\cdot (1213)^{\star }B^{\pm }\cdot (1023)^{\star }\Phi =(1123)^{\star }\Phi \cdot (1233)^{\star }B^{\pm }$.
  • $B^{\pm }$ in terms of $\Phi$ and $R$ and $R$ in terms of $T$.
  • R3, R2, R1
  • Symmetry of $\Phi$ and of $B^{\pm }$.
  • $u$, $d$ and $\#$
  • Idempotence for $T$, $R$, $\Phi$ and $B^{\pm }$.