We determine the L_ ∞ L∞-algebra that controls deformations of a relative Rota–Baxter Lie
algebra and show that it is an extension of the dg Lie algebra controlling deformations of the …

Rational homotopy theory is a branch of topology which studies the “non-torsion” behaviour
of the homotopy type of topological spaces. This area was born about fifty years ago in …

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 first construct the controlling algebras of embedding tensors and Lie–
Leibniz triples, which turn out to be a graded Lie algebra and an L_ ∞ L∞-algebra …

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 …

In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer
pairs. We give the cohomology of pre-LieDer pairs by using the twist $ L_\infty $-algebra of …

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 …

We study the shifted analogue of the “Lie–Poisson” construction for L_ ∞ L∞ algebroids
and we prove that any L_ ∞ L∞ algebroid naturally gives rise to shifted derived Poisson …