Homotopy graph-complex for configuration and knot spaces

DOI10.1090/S0002-9947-08-04650-3zbMath1158.57030arXivmath/0611766MaRDI QIDQ3600635

Pascal Lambrechts, Victor Tourtchine

Publication date: 5 February 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611766

zbMATH Keywords

primitive elementembedding calculusknot spaceBousfield-Kan spectral sequencegraph-complex

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Embeddings in differential topology (57R40) Immersions in differential topology (57R42) Spectral sequences in algebraic topology (55T99) Loop space machines and operads in algebraic topology (55P48)

Related Items

Milnor invariants of string links, trivalent trees, and configuration space integrals, The rational homology of spaces of long knots in codimension \(> 2\), Multiple edges in M. Kontsevich's graph complexes and computations of the dimensions and Euler characteristics, Differentials on graph complexes, Cosimplicial models for spaces of links, Graph-complexes computing the rational homotopy of high dimensional analogues of spaces of long knots, Cyclic operad formality for compactified moduli spaces of genus zero surfaces, M. Kontsevich's graph complex and the Grothendieck-Teichmüller Lie algebra

Cites Work

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• The rational homology of spaces of long knots in codimension \(> 2\)
• Lie coalgebras and rational homotopy theory. I: Graph coalgebras
• Coformality and rational homotopy groups of spaces of long knots
• Moduli of graphs and automorphisms of free groups
• Perturbative series and the moduli space of Riemann surfaces
• Operads and motives in deformation quantization
• Infinitesimal operations on complexes of graphs
• A one-dimensional embedding complex
• On the Vassiliev knot invariants
• Configuration spaces and Vassiliev classes in any dimension
• Deformation quantization of Poisson manifolds
• On a theorem of Kontsevich
• Graph complexes in deformation quantization
• Calculus of functors, operad formality, and rational homology of embedding spaces
• Formality of the little N-disks operad
• Operads and knot spaces
• Knots, operads, and double loop spaces
• ON THE OTHER SIDE OF THE BIALGEBRA OF CHORD DIAGRAMS
• Homotopy approximations to the space of knots, Feynman diagrams, and a conjecture of Scannell and Sinha
• Modular operads
• Koszul Resolutions
• ALGEBRAIC STRUCTURES ON GRAPH COHOMOLOGY