On the homology of the spaces of long knots

Details On the homology of the spaces of long knots On the homology of the spaces of long knots

2001-05-16

arxiv.org/abs/math/0105140v1

Mathematics

Quantum Algebra

27pages, 7figures

Scientific paper

This paper is a little more detailed version of math-QA/0010017 "Sur l'homologie des espaces de n\oe uds non-compacts", where the first term of the Vassiliev spectral sequence (computing the homology of the space of long knots in ${\mathbb R}^d$, $d\ge 3$) was described in terms of the Hochschild homology of the Poisson algebras operad for $d$ odd, and of the Gerstenhaber algebras operad for $d$ even. In particular, the bialgebra of chord diagrams arises as some subspace of this homology. The homology in question is the space of characteristic classes for Hochschild cohomology of Poisson (resp. Gerstenhaber) algebras considered as associative algebras. The paper begins with necessary preliminaries on operads. Also a simplification of the computations of the first term of the Vassiliev spectral sequence is given.

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