BV-structures on the homology of the framed long knot space

Abstract

We introduce BV-algebra structures on the homology of the space of framed long knots in ${\mathbb{R}}^n$ in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology. The second one is defined on the Hochschild homology associated with a cyclic, multiplicative operad of graded modules. The latter can be applied to Bousfield-Salvatore spectral sequence converging to the homology of the space of framed long knots. Conjecturally these two structures coincide with each other.

13 pages, 3 figures, to appear in Journal of Homotopy and Related Structures

References in corpus (2)

• Long knots and maps between operads
• Poisson structures on the homology of the space of knots

Cited by in corpus (1)

• The Fox-Hatcher cycle and a Vassiliev invariant of order three