A homological definition of the Jones polynomial

Details A homological definition of the Jones polynomial A homological definition of the Jones polynomial

2002-01-23

arxiv.org/abs/math/0201221v2

Geom. Topol. Monogr. 4 (2002) 29-41

Mathematics

Geometric Topology

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper3.abs.html

Scientific paper

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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