A homological definition of the Jones polynomial
Stephen Bigelow
Abstract
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 B2n. We define a covering space tildeC of the space of unordered n-tuples of distinct points in the 2n-punctured disk. We then describe two n-manifolds tildeS and tildeT in tildeC, and show that the Jones polynomial of L can be defined as an intersection pairing between tildeS and beta tildeT. Our construction is similar to one given by Lawrence, but more concrete.
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