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Abstract
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We give a new definition of the knot invariant associated to the Lie algebra
. Knowing
these for all
is equivalent to knowing the HOMFLY polynomial. Our definition requires that the knot
or link be presented as the plat closure of a braid. The invariant is then a homological
intersection pairing between two immersed manifolds in a configuration space of
points in a disk. This generalizes previous work on the Jones polynomial, which is the
case .
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Keywords
HOMFLY polynomial, braid group, plat closure, bridge
position, configuration space
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 20F36
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Publication
Received: 23 August 2006
Revised: 14 September 2007
Accepted: 14 September 2007
Published: 15 October 2007
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