Notes for AKT-090917-2/0:09:48: Difference between revisions
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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. |
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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. |
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Revision as of 01:16, 19 September 2009
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 for union of circles give explicitly for any knots.
