Sur l'homologie des espaces de noeuds non-compacts

2000/10/02 by Victor Tourtchine, Tourtchine, Victor
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AT #math.QA

paper · pdf · doi:10.48550/arxiv.math/0010017

32 pages, 6 figures, in French

arxiv created 2000/10/02 · arxiv updated 2009/11/30

Abstract

The spectral sequence constructed by V.A.Vassiliev computes the homology of the spaces of non-compact knots in \bf R^d, d≥ 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.

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