Towards Noncommutative Linking Numbers via the Seiberg-Witten Map

Figure 1

The figure accounts the computation at the first order in of the linking number. For the case of knots in it is observed at this order that the noncommutativity induces the existence of 6 different knots, represented in the simplest case by circles of different colors , that intersect the original trivial homology -cycle . At the th order there will be knots intersecting . In the general case the knots would be real knots linked, for instance, the trefoil or even more complicated knots.