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.
Keywords
Jones polynomial, braid group, plat
closure, bridge position
