Date(s)

Link(s)

2010/02/22

???

2010/01/20

Formal integration

2010/01/13

Combing wB

2010/01/06

Exponentiation in tder

2009/09/22

descending vknots

2009/08/26

red over green vtangles

2009/08/19

Polyak Algebra

2009/07/08

Immanants

2009/07/01

Alexander modules

2009/06/24

Alexander modules

2009/06/10

Alexander, PBW for A^w, class videos

2009/06/03

Low key

2009/05/06

Low key

2009/04/29

Winter on Ribbons

2009/04/22

Misc

2009/04/15

KV

2009/03/25

KV

2009/03/18

Peter Lee

2009/03/04

Kirby calculus

2009/02/25

Karene on ReidemeisterSchreier

2009/02/11

Dror on Trotter, Jana on Alexander

2009/02/04

Bracelets

2009/01/28

gl(N) chickens

2009/01/15

2D Gauss Diagrams, FiC

2009/01/08

S&G update and more

2008/12/11

Chu on Garside, II

2008/12/04

wZ is 11

2008/11/27

The Wen

2008/11/20

The Zoom Space

2008/11/13

Chu on Garside

2008/11/06

Z and GPV

2008/10/30

Peter Lee on EHKR

2008/10/23

Map of the Field

2008/09/25

Hirasawa on Open Books

2008/09/18

Odd Khovanov

2008/09/17

Categorification.m

2008/09/11

More wAlex

2008/09/03

?

2008/08/27

Dexp and BCH

2008/08/06

Z, A, det, tr, log

2008/07/30

Alexander Relations Marathon

2008/07/02

Peter Lee on horizontal Aw

2008/06/25

wAlexander

2008/06 1622

Thomas Fiedler Marathon

2008/06/11

?

2008/06/04

Dylan Thurston

2008/05/28

Welded Tangles

2008/05/21

Bruce, Lucy

2008/04/23

Welded Knots

2008/04/16

Quandles and Lie algebras

2008/04/09

Nodiv AlekseevTorossian

2008/04/02

Knotted Kung Fu Pandas

2008/03/26

Homotopy invariants

2008/03/19

Infinitesimal Artin

2008/03/12

Infinitesimalization of Artin

2008/03/05

Krzysztof Putyra on Odd Khovanov Homology

2008/02/27

Karene Chu on Proof of Artin

2008/02/20

Organizational, Hecke algebras

2008/02/13

Exponential and Magnus expansions

2008/02/06

cancelled

2008/01/30

Artin's theorem

2008/01/16

Hutchings' work, 2

2008/01/09

Hutchings' work, 1

2007/12/12

Bone soup

2007/12/05

Expansions

2007/11/28

Quantum groups

2007/11/21

Surfaces and gl(N)/so(N)

2007/11/07

Expansions for Groups

2007/10/31

Louis Leung on bialgebra weight systems

2007/10/24

Zsuzsi Dancso, continued

2007/10/17

Jana Archibald on the multivariable Alexander

2007/10/10

Zsuzsi Dancso on diagrammatic su(2)

2007/10/03

Hernando Burgos on alternating tangles

2007/09/26

Peter Lee on homology

2007/09/06

Garoufalidis' visit

2007/08/30

Art and enumeration

2007/08/23

My Hanoi talk?

2007/08/16

Lie bialgebra weight systems and more

2007/07/19

Subdiagram formulas

2007/07/12

Playing with Brunnians

2007/07/05

Virtualization

2007/06/28

Virtual braids

2007/06/07

Virtual knots

2007/05/31

Social gathering

2007/05/24

Lee on Frozen Feet


The Plan
See The Proposed Thomas Fiedler Marathon.
Fiedler's Abstract
Title : A candidate for a calculable complete invariant for classical knots
Abstract :
To each oriented classical knot K and each natural number n one can
associate an isotopy class of a (n,n)tangle which is an isotopy
invariant of K.
We construct two combinatorial relative 1cocycles, called Y and Sing,
for spaces of tangels. The cocycle Y takes values in a Hecke algebra
H_n+1 with coefficients in a polynomial ring of three variables. The
cocycle Sing takes values in a module
(over some polynomial ring) freely generated by all 1singular tangels.
For each 1singular tangle we can consider its two nonsingular
resolutions and we can apply the cocycle Y to these resolutions.
Iterating this proces, with starting point the above (n,n)tangle,
creates a "wave" in Hecke algebras of increasing dimension. We show that
this wave is indeed "expanding" and it is a good candidate for a
complete knot invariant.
The cours will be structured as follows:
basic notions from singularity theory and a higher order Reidemeister
theorem
construction of polynomial valued 1cocycles for knot spaces. The
tetrahedron and the cube equations. Calculations
integervalued 1cocycles for closed braids and a new filtration on the
space of all finite type invariants for closed braids
essential homotopies of knots and their 1cocycle. Specific invariants
for knots of unknotting number one.
Content
Blackboard shots are at BBS/Fiedler080616084319.jpg. The programs written and a very condensed summary of our results are at Odds, Ends, Unfinished: Some HOMFLYPT One Parameter Knot Theory Computations.