| 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 v-knots
|
| 2009/08/26
|
red over green v-tangles
|
| 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 Reidemeister-Schreier
|
| 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 1-1
|
| 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
|
w-Alexander
|
| 2008/06 16-22
|
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
|
No-div Alekseev-Torossian
|
| 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 1-cocycles, 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 1-singular tangels.
For each 1-singular tangle we can consider its two non-singular
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 1-cocycles for knot spaces. The
tetrahedron and the cube equations. Calculations
-integer-valued 1-cocycles for closed braids and a new filtration on the
space of all finite type invariants for closed braids
-essential homotopies of knots and their 1-cocycle. Specific invariants
for knots of unknotting number one.
Content
Blackboard shots are at BBS/Fiedler-080616-084319.jpg. The programs written and a very condensed summary of our results are at Odds, Ends, Unfinished: Some HOMFLY-PT One Parameter Knot Theory Computations.
