Knot at Lunch on June 16-22 - Revision history

Drorbn: Knot at Lunch on June 16-20 moved to Knot at Lunch on June 16-22

2008-06-23T13:34:26Z

Knot at Lunch on June 16-20 moved to Knot at Lunch on June 16-22

← Older revision

Revision as of 09:34, 23 June 2008

Drorbn: /* Content */

2008-06-21T22:06:50Z

Content

← Older revision		Revision as of 18:06, 21 June 2008
Line 38:		Line 38:
	==Content==		==Content==

	Blackboard shots are at {{BBS Link\|Fiedler-080616-084319.jpg}}.		Blackboard shots are at {{BBS Link\|Fiedler-080616-084319.jpg}}. The programs written and a very condensed summary of our results are at {{Home Link\|Misc/OneParameter/OneParameterY.html\|Odds, Ends, Unfinished: Some HOMFLY-PT One Parameter Knot Theory Computations}}.

Drorbn at 14:02, 16 June 2008

2008-06-16T14:02:28Z

← Older revision		Revision as of 10:02, 16 June 2008
Line 35:		Line 35:
	for knots of unknotting number one.		for knots of unknotting number one.
	</pre>		</pre>

			==Content==

			Blackboard shots are at {{BBS Link\|Fiedler-080616-084319.jpg}}.

Drorbn at 19:55, 7 April 2008

2008-04-07T19:55:37Z

New page

{{KAL/Navigation}}

==The Plan==
See [[Knot at Lunch on February 20 2008#The_Proposed_Thomas_Fiedler_Marathon|The Proposed Thomas Fiedler Marathon]].

==Fiedler's Abstract==

<pre>
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.
</pre>