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

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

2011-10-11

arxiv.org/abs/1110.2358v1

Mathematics

Geometric Topology

9 pages, 2 figures

Scientific paper

We introduce BV-algebra structures on the homology of the space of framed long knots in 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 over graded modules. The latter can be applied to a certain 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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