A homological definition of the Jones polynomial

Stephen Bigelow

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A homological definition of the Jones polynomial

Stephen Bigelow

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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 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.

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BibTeX RIS

Stephen Bigelow. 2002-11-15. A homological definition of the Jones polynomial. https://arxiv.org/abs/math/0201221

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