131 citations · 651 across the 67 of their papers we have counts for
9 papers · 1 filter
Deformation theory of Lie bialgebra properads
Sergei Merkulov, Thomas Willwacher
We compute the homotopy derivations of the properads governing even and odd Lie bialgebras as well as involutive Lie bialgebras. The answer may be expressed in terms of the Kontsev…
On quantizable odd Lie bialgebras
Anton Khoroshkin, Sergei Merkulov, Thomas Willwacher
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The ma…
Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves
Sergei Merkulov, Thomas Willwacher
We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves (which, according to Penner, i…
Differentials on graph complexes II - hairy graphs
Anton Khoroshkin, Thomas Willwacher, Marko Živković
We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spect…
Hochschild-Pirashvili homology on suspensions and representations of
Victor Turchin, Thomas Willwacher
We show that the Hochschild-Pirashvili homology on any suspension admits the so called Hodge splitting. For a map between suspensions , the induced map in the Hoc…
Deformation quantization and the Gerstenhaber structure on the homology of knot spaces
Thomas Willwacher
It is well known that (in suitable codimension) the spaces of long knots in modulo immersions are double loop spaces. Hence the homology carries a natural Gerstenhab…
Models for the n-Swiss Cheese operads
Thomas Willwacher
We describe combinatorial Hopf (co-)operadic models for the Swiss Cheese operads built from Feynman diagrams. This extends previous work of Kontsevich and Lambrechts-Volić for the…
Chern-Simons forms and higher character maps of Lie representations
Yuri Berest, Giovanni Felder, Sasha Patotski +2
This paper is a sequel to our earlier work [BFPRW], where we study the derived representation scheme DRep_{g}(A) parametrizing the representations of a Lie algebra A in a finite-di…
The intrinsic formality of -operads
Benoit Fresse, Thomas Willwacher
We establish that -operads satisfy a rational intrinsic formality theorem for . We gain our results in the category of Hopf cooperads in cochain graded dg-modules whi…