The rational homology of spaces of long knots in codimension > 2
By P. Lambrechts, Victor Tourtchine, Ismar Volic. 2007
55 citations recorded by the source corpus.
We determine the rational homology of the space of long knots in R for d 4 . Our main result is that the Vassiliev spectral sequence computing this rational homology collapses at the E page. As a corollary we get that the homology of long knots (modulo immersions) is the Hochschild homology of the Poisson algebras operad with bracket of degree d 1 , which can be obtained as the homology of an explicit graph complex and is in theory completely computable.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e904455cb8df4c8e142c4fe4a04419099a8077f1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
- G. Arone
- Victor Turchin
- B. Munson
- Ismar Volic
- Thomas Willwacher
- Dev Sinha
- Benoit Fresse
- Victor Tourtchine
In Mathematical Physics
- G. Arone
- Victor Turchin
- B. Munson
- Ismar Volic
- Thomas Willwacher
- Dev Sinha
- Benoit Fresse
- Victor Tourtchine
Citations in the corpus
- Cubical Homotopy Theory (2015, background): “28 ([LTV10], Lemma 4.”
- Graph-complexes computing the rational homotopy of high dimensional analogues of spaces of long knots (2011, background): “Indeed, the complex Der ( Assoc i∗ −→ H∗(Bm,Q) ) is the usual Hochschild complex of the operad H∗(Bn,Q) = Poissn−1, see [19, 37, 21].”