English

Sur l'homologie des espaces de noeuds non-compacts

Quantum Algebra 2007-05-23 v1 Algebraic Topology

Abstract

The spectral sequence constructed by V.A.Vassiliev computes the homology of the spaces of non-compact knots in Rd{\bf R}^d, d3d\ge 3. In this work the first term of this spectral sequence is described in terms of the homology of the Hochschild complex for the Poisson algebras operad, if d is odd (resp. for the Gerstenhaber algebras operads, if d is even). In particular the bialgebra of chord diagrams arises as some subspace of this homology (in this case d=3). Also a simplification for the calculation of the Vassiliev spectral sequence in the first term is provided.

Keywords

Cite

@article{arxiv.math/0010017,
  title  = {Sur l'homologie des espaces de noeuds non-compacts},
  author = {Victor Tourtchine},
  journal= {arXiv preprint arXiv:math/0010017},
  year   = {2007}
}

Comments

32 pages, 6 figures, in French