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

Keiichi Sakai

doi:10.1007/s40062-015-0111-1

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arXiv · 1110.2358

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

Keiichi Sakai

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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.

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Keiichi Sakai. 2015-05-11. BV-structures on the homology of the framed long knot space. https://doi.org/10.1007/s40062-015-0111-1

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