||Videos, Notes, and Links
||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.
|| 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.
|| 090922: FI, 4T, HOMFLY and FI and 4T, statement of the Fundamental Theorem, framed knots.|
090924-1: Some dimensions of , is a commutative algebra, .
090924-2: is a co-commutative algebra, the relation with products of invariants, is a bi-algebra.
||Homework Assignment 1|
Homework Assignment 1 Solutions
090929: The Milnor-Moore theorem, primitives, the map .
091001-1: Jacobi diagrams, AS, IHX, STU, and the equivalence of all that with 4T.
091001-2: The very basics on Lie algebras.
|| 091006: Lie algebraic weight systems, .|
091008-1: More on , Lie algebras and the four colour theorem.
091008-2: The "abstract tenssor" approach to weight systems, and PBW, the map .
|| 091013: Algebraic properties of vs. algebraic properties of .|
Thursday's class canceled.
|| 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.
|| 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).
|| 091103: The details of .|
091105-1: Three basic problems: genus, unknotting numbers, ribbon knots.
091105-2: The three basic problems and algebraic knot theory.
|| 091110: Tangles and planar algebras, shielding and the generators of KTG.|
Homework Assignment 3
No Thursday class.
||Local Khovanov Homology|
091119-1: Local Khovanov homology, I.
091119-2: Local Khovanov homology, II.
|| 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.
|| 091201: The relations in KTG.|
091203-1: The Existence of the Exponential Function.
091203-2: The Final Exam, Dror's failures.
||The Final Exam on Thu Dec 10, 9-11, Bahen 6183.
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Algebraic Knot Theory
Department of Mathematics, University of Toronto, Fall 2009
Agenda: Understand "(u, v, and w knots) x (topology, combinatorics, low algebra, and high algebra)". Understand the promise and the difficulty of the not-yet-existant "Algebraic Knot Theory".
Instructor: Dror Bar-Natan, email@example.com, Bahen 6178, 416-946-5438. Office hours: Wednesdays 10:30-11:30 at Bahen 6178 (on teaching weeks), or, if truly impossible, by appointment.
Classes: Tuesdays 10-11 in 215 Huron room 1018 and Thursdays 9-11 in Bahen 6183.