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A homological definition of the HOMFLY polynomial
Stephen Bigelow
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Algebraic & Geometric Topology 7
(2007) 1409–1440
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Abstract
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We give a new definition of the knot invariant
associated to the Lie algebra suN+1.
Knowing these for all N 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 N=1.
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Keywords
HOMFLY polynomial, braid group, plat
closure, bridge position, configuration space
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Mathematical Subject Classification
Primary: 57M25
Secondary: 20F36, 57M27
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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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