We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the
Grothendieck–Teichmüller Lie algebra grt _1 grt 1. The map is explicitly described. This …

We express the rational homotopy type of the mapping spaces $\mathrm {Map}^ h (\mathsf
D_m,\mathsf D_n^{\mathbb Q}) $ of the little discs operads in terms of graph complexes …

In this paper we consider L∞-algebras equipped with complete descending filtrations. We
prove that, under some mild conditions, an L∞ quasi-isomorphism U: L→ L˜ induces a weak …

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 …

This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry,
topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment …

We construct a real combinatorial model for the configuration spaces of points of compact
smooth oriented manifolds without boundary. We use these models to show that the real …

We establish that En-operads satisfy a rational intrinsic formality theorem for n≥ 3. We get
our results in the category of Hopf cooperads in cochain graded dg-modules which defines a …

We prove the validity over RR of a commutative differential graded algebra model of
configuration spaces for simply connected closed smooth manifolds, answering a conjecture …

Abstract In paper [4], we constructed a symmetric monoidal category S Lie∞ MC whose
objects are shifted (and filtered) L∞-algebras. Here, we fix a cooperad C and show that …

Covering an exceptional range of topics, this text provides a unique overview of the Maurer-
Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new …