Geodesic
A homological definition of the HOMFLY polynomial
Bigelow, Stephen1
1Department of Mathematics, University of California at Santa Barbara, California 93106, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1409-1440
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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.

DOI : 10.2140/agt.2007.7.1409
Keywords: HOMFLY polynomial, braid group, plat closure, bridge position, configuration space

Bigelow, Stephen  1

1 Department of Mathematics, University of California at Santa Barbara, California 93106, USA 
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Bigelow, Stephen. A homological definition of the HOMFLY polynomial. Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1409-1440. doi: 10.2140/agt.2007.7.1409

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