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

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. [ABSTRACT FROM AUTHOR]