slide: PDF.

video: comming soon.

abstract:

I will introduce two (possibly the same) BV-algebra structures on the homology of the space \(K\) of framed long knots. The first one is a direct analogue to Chas-Sullivan's string topology. The second one is described on the Hochschild homology associated with any cyclic, multiplicative operad of graded modules. The latter is a graded version of Tradler's BV-structure, and can be applied to \(E^2\)-term of the Goodwillie-Sinha-Salvatore spectral sequence converging to \(H_*(K)\).