Notes for AKT-090917-2/0:09:48 - Revision history

Iva at 14:05, 8 September 2011

2011-09-08T14:05:12Z

← Older revision		Revision as of 10:05, 8 September 2011
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	~~Def~~: A knot diagram is '''descending''' if there exists a point on the diagram ~~s.t.~~ ~~if we draw the knot~~ starting at that point, ~~whenever~~ the knot ~~has~~ a crossing, the ~~new~~ ~~segment~~ ~~goes~~ ~~under~~ the ~~existing~~ ~~segment~~.		''Definition'': A knot diagram is '''descending''' if there exists a point on the diagram such that, starting from that point and going along the knot, each time we reach any crossing for the first time we do so along the upper strand of the crossing.

	By flipping crossings one can make any knot descending and any descending ~~knots~~ ~~are~~ ~~unknots~~. ~~Deduce~~ that the Jones skein relation and value of <math>J</math> for union of ~~circles~~ give <math>J</math> explicitly for any ~~knots~~.		By flipping crossings one can make any knot descending and any descending knot is the unknot. From this we can deduce that the Jones skein relation and the value of <math>J</math> for the union of any number unknots give <math>J</math> explicitly for any knot.

Conan777 at 06:16, 19 September 2009

2009-09-19T06:16:47Z

← Older revision		Revision as of 02:16, 19 September 2009
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	Def: A knot diagram is '''descending''' if there exists a point on the diagram s.t. if we draw the knot starting at that point, whenever the knot has a crossing, the new segment goes under the existing segment.		Def: A knot diagram is '''descending''' if there exists a point on the diagram s.t. if we draw the knot starting at that point, whenever the knot has a crossing, the new segment goes under the existing segment.

			By flipping crossings one can make any knot descending and any descending knots are unknots. Deduce that the Jones skein relation and value of <math>J</math> for union of circles give <math>J</math> explicitly for any knots.

Conan777 at 06:12, 19 September 2009

2009-09-19T06:12:29Z

New page

Def: A knot diagram is '''descending''' if there exists a point on the diagram s.t. if we draw the knot starting at that point, whenever the knot has a crossing, the new segment goes under the existing segment.