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A homological definition of the Jones polynomial
Stephen Bigelow
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Geometry & Topology Monographs 4
(2002) 29–41
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Abstract
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We give a new definition of the Jones polynomial. Let L be an
oriented knot or link obtained as the plat closure of a braid β
∈ B2n. We define a covering space C of the space of
unordered n–tuples of distinct points in the 2n–punctured disk.
We then describe two n–manifolds S and T in
C, and show that the Jones polynomial of L can be defined
as an intersection pairing between S and βT.
Our construction is similar to one given by Lawrence, but more concrete.
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Keywords
Jones polynomial, braid group, plat
closure, bridge position
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Mathematical Subject Classification
Primary: 57M25
Secondary: 20F36, 57M27
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Publication
Received: 30 November 2001
Revised: 4 April 2002
Accepted: 22 July 2002
Published: 19 September 2002
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