||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.
|Register of Good Deeds / To Do List
Add your name / see who's in!
Solve the following problems and submit them in class by December 1, 2009:
Problem 1 With , and as below, write as a composition of and two 's, using he basic TG operations , , and .
Problem 2 Show that the "topological boundary" operator and the "crossing change" operator of the class of November 5 are compositions of the basic TG operations , , and (you are also allowed to use "nullary" operations, otherwise known as "constants").
Problem 3 Write the third Reidemeister move R3 as a relation on .