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21. 3. 2007.
The rational homology of spaces of long knots in codimension > 2
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.