AKT-09/Navigation

#	Week of...	Videos, Notes, and Links
1	Sep 7	About This Class  090910-1: 3-colourings, Reidemeister's theorem, invariance, the Kauffman bracket.  090910-2: R23 invariance of the bracket, R1, the writhe, the Jones polynomial, programming the Jones polynomial. Tricolourability
2	Sep 14	090915: More on Jones, some pathologies and more on Reidemeister, our overall agenda.  090917-1: The definition of finite type, weight systems, Jones is a finite type series.  090917-2: The skein relation for Jones; HOMFLY-PT and Conway; the weight system of Jones.
3	Sep 21	090922: FI, 4T, HOMFLY and FI and 4T, statement of the Fundamental Theorem, framed knots.  090924-1: Some dimensions of ${\mathcal {A}}_{n}$, ${\mathcal {A}}$ is a commutative algebra, ${\mathcal {A}}(\bigcirc )\equiv {\mathcal {A}}(\uparrow )$. Class Photo  090924-2: ${\mathcal {A}}$ is a co-commutative algebra, the relation with products of invariants, ${\mathcal {A}}$ is a bi-algebra.
4	Sep 28	Homework Assignment 1 Homework Assignment 1 Solutions  090929: The Milnor-Moore theorem, primitives, the map ${\mathcal {A}}^{r}\to {\mathcal {A}}$.  091001-1: Jacobi diagrams, AS, IHX, STU, and the equivalence of all that with 4T.  091001-2: The very basics on Lie algebras.
5	Oct 5	091006: Lie algebraic weight systems, $gl_{N}$.  091008-1: More on $gl_{N}$, Lie algebras and the four colour theorem.  091008-2: The "abstract tenssor" approach to weight systems, ${\mathcal {U}}({\mathfrak {g}})$ and PBW, the map ${\mathcal {T}}_{\mathfrak {g}}$.
6	Oct 12	091013: Algebraic properties of ${\mathcal {U}}({\mathfrak {g}})$ vs. algebraic properties of ${\mathcal {A}}$. Thursday's class canceled.
7	Oct 19	091020: Universal finite type invariants, filtered and graded spaces, expansions. Homework Assignment 2 The Stonehenge Story  091022-1: The Stonehenge Story to IHX and STU.  091022-2: The Stonhenge Story: anomalies, framings, relation with physics.
8	Oct 26	091027: Knotted trivalent graphs and their chord diagrams.  091029-1: Zsuzsi Dancso on the Kontsevich Integral (1).  091029-2: Zsuzsi Dancso on the Kontsevich Integral (2).
9	Nov 2	091103: The details of ${\mathcal {A}}^{TG}$.  091105-1: Three basic problems: genus, unknotting numbers, ribbon knots.  091105-2: The three basic problems and algebraic knot theory.
10	Nov 9	091110: Tangles and planar algebras, shielding and the generators of KTG. Homework Assignment 3 No Thursday class.
11	Nov 16	Local Khovanov Homology  091119-1: Local Khovanov homology, I.  091119-2: Local Khovanov homology, II.
12	Nov 23	091124: Emulation of one structure inside another, deriving the pentagon.  091126-1: Peter Lee on braided monoidal categories, I.  091126-2: Peter Lee on braided monoidal categories, II.
13	Nov 30	091201: The relations in KTG.  091203-1: The Existence of the Exponential Function.  091203-2: The Final Exam, Dror's failures.
F	Dec 7	Final on Thu Dec 10, 9-11, Bahen 6183.
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