Differentials on graph complexes
A Khoroshkin, T Willwacher, M Živković - Advances in Mathematics, 2017 - Elsevier
We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by
M. Kontsevich. We construct spectral sequences converging to zero whose first page …
M. Kontsevich. We construct spectral sequences converging to zero whose first page …
The frobenius properad is koszul
We show the Koszulness of the properad governing involutive Lie bialgebras and also of the
properads governing nonunital and unital-counital Frobenius algebras, solving a long …
properads governing nonunital and unital-counital Frobenius algebras, solving a long …
Deformation theory of Lie bialgebra properads
S Merkulov, T Willwacher - arXiv preprint arXiv:1512.05252, 2015 - arxiv.org
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 …
bialgebras as well as involutive Lie bialgebras. The answer may be expressed in terms of …
Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves
S Merkulov, T Willwacher - arXiv preprint arXiv:1511.07808, 2015 - arxiv.org
We establish a new and surprisingly strong link between two previously unrelated theories:
the theory of moduli spaces of curves ${\mathcal M} _ {g, n} $(which, according to Penner, is …
the theory of moduli spaces of curves ${\mathcal M} _ {g, n} $(which, according to Penner, is …
Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs
M Živković - arXiv preprint arXiv:1703.09605, 2017 - arxiv.org
We construct a direct quasi-isomorphism from Kontsevich's graph complex GC_n to the
oriented graph complex OGC_ {n+ 1}, thus providing an alternative proof that the two …
oriented graph complex OGC_ {n+ 1}, thus providing an alternative proof that the two …
Classification of universal formality maps for quantizations of Lie bialgebras
S Merkulov, T Willwacher - Compositio Mathematica, 2020 - cambridge.org
We settle several fundamental questions about the theory of universal deformation
quantization of Lie bialgebras by giving their complete classification up to homotopy …
quantization of Lie bialgebras by giving their complete classification up to homotopy …
Grothendieck-Teichmüller group, operads and graph complexes: a survey
S Merkulov - arXiv preprint arXiv:1904.13097, 2019 - arxiv.org
arXiv:1904.13097v3 [math.QA] 18 Jul 2021 Page 1 arXiv:1904.13097v3 [math.QA] 18 Jul
2021 GROTHENDIECK-TEICHMULLER GROUP, OPERADS AND GRAPH COMPLEXES: A …
2021 GROTHENDIECK-TEICHMULLER GROUP, OPERADS AND GRAPH COMPLEXES: A …
From deformation theory of wheeled props to classification of Kontsevich formality maps
A Andersson, S Merkulov - International Mathematics Research …, 2022 - academic.oup.com
We study the homotopy theory of the wheeled prop controlling Poisson structures on formal
graded finite-dimensional manifolds and prove, in particular, that the Grothendieck …
graded finite-dimensional manifolds and prove, in particular, that the Grothendieck …
Stable cohomology of polyvector fields
T Willwacher - arXiv preprint arXiv:1110.3762, 2011 - arxiv.org
arXiv:1110.3762v4 [math.QA] 3 Dec 2014 Page 1 arXiv:1110.3762v4 [math.QA] 3 Dec 2014
STABLE COHOMOLOGY OF POLYVECTOR FIELDS THOMAS WILLWACHER Abstract. We …
STABLE COHOMOLOGY OF POLYVECTOR FIELDS THOMAS WILLWACHER Abstract. We …
Multi-directed graph complexes and quasi-isomorphisms between them II: Sourced graphs
M Živković - International Mathematics Research Notices, 2021 - academic.oup.com
We prove that the projection from graph complex with at least one source to oriented graph
complex is a quasi-isomorphism, showing that homology of the “sourced” graph complex is …
complex is a quasi-isomorphism, showing that homology of the “sourced” graph complex is …