22 citations · 39 across the 9 of their papers we have counts for
9 papers
Delooping totalization of a multiplicative operad
Victor Tourtchine
The paper shows that under some conditions the totalization of a cosimplicial space obtained from a multiplicative operad is a double loop space of the space of derived morphisms f…
Hodge decomposition in the homology of long knots
Victor Tourtchine
The paper describes a natural splitting in the rational homology and homotopy of the spaces of long knots. This decomposition presumably arises from the cabling maps in the same wa…
Coformality and the rational homotopy groups of spaces of long knots
Gregory Arone, Pascal Lambrechts, Victor Tourtchine +1
We show that the Bousfield-Kan spectral sequence which computes the rational homotopy groups of the space of long knots in , where , collapses at the p…
Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces
P. Lambrechts, V. Tourtchine, I. Volic
As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or o…
Homotopy graph-complex for configuration and knot spaces
Pascal Lambrechts, Victor Tourtchine
In the paper we prove that the primitive part of the Sinha homology spectral sequence E^2-term for the space of long knots is rationally isomorphic to the homotopy E^2-term. We als…
What is 1-term relation for higher homology of long knots
Victor Tourtchine
Vassiliev's spectral sequence for long knots is discussed. Briefly speaking we study what happens if the strata of non-immersions are ignored. Various algebraic structures on the s…