INVARIANTS OF CLOSED BRAIDS VIA COUNTING SURFACES
2013 ◽
Vol 22
(03)
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pp. 1350011
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Keyword(s):
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we present simple formulas for an infinite family of invariants in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram associated with a closed braid. We then identify the resulting invariants with partial derivatives of the HOMFLY-PT polynomial.
2005 ◽
Vol 49
(3)
◽
pp. 305-321
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Keyword(s):
2007 ◽
Vol 221
(12)
◽
pp. 1701-1715
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2007 ◽
Vol 359
(6)
◽
pp. 2675-2686
◽
1988 ◽
Vol 31
(2)
◽
pp. 159-167
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Keyword(s):