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

Sakai, Keiichi

11 ( 3 )  , pp.425 - 441 , 2015-05-27 , SPRINGER HEIDELBERG
We introduce BV-algebra structures on the homology of the space of framed long knots in Rn in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology [5]. 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.

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