A homological definition of the Jones polynomial
Abstract
Description
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 beta in B_{2n}. We define a covering space tilde{C} of the space of unordered n-tuples of distinct points in the 2n-punctured disk. We then describe two n-manifolds tilde{S} and tilde{T} in tilde{C}, and show that the Jones polynomial of L can be defined as an intersection pairing between tilde{S} and beta tilde{T}. Our construction is similar to one given by Lawrence, but more concrete.
Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper3.abs.html
Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper3.abs.html