Related papers: Polydifferential Lie bialgebras and graph complexe…
We introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it is motivated by works of Harer, Mosher and Penner. Using…
We give a new CR invariant treatment of the bigraded Rumin complex and related cohomology groups via differential forms. A key benefit is the identification of balanced $A_\infty$-structures on the Rumin and bigraded Rumin complexes. We…
In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral…
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…
In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology,…
We introduce a new space of generalized functions of bounded deformation $GBD_{F}$, made of functions u whose one-dimensional slice $u(\gamma) \cdot \dot{\gamma}$ has bounded variation in a generalized sense for all curves $\gamma$ solution…
In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…
This paper gives a canonical construction, in terms of additive cohomological functors, of the universal formal deformation of a compact complex manifold without vector fields (more generally of a faithful $g$-module, where $g$ is a sheaf…
Although the deformation of the Heisenberg algebra by a minimal length has become a central tool in quantum gravity phenomenology, it has never been rigorously obtained and is often derived using heuristic reasoning. In this study, we move…
We introduce a diagram category, study its structure, and investigate some of its applications to the representation theory of Lie algebras and Lie superalgebras. The morphisms of the category, which contains a subcategory isomorphic to the…
The notion of singular one-parameter deformation of a Lie algebra is introduced. It is shown that the complex infinite-dimensional Lie algebra of polynomial vector fields in C with trivial 1-jet at the origin has such singular deformation.
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We describe various nonrelativistic contractions of two classes of twisted Poincare algebra: canonical one ($\theta_{\mu\nu}$-deformation) and the one leading to Lie-algebraic models of noncommutative space-times. The cases of…
In this paper, we classify the algebraic isomonodromic deformations that can be obtained through restriction to generic lines of logarithmic flat connections on the complex projective plane $\mathbb{P}^2_\mathbb{C}$ whose singular locus is…
This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected…
A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how…
We say that a formal deformation from an algebra $N$ to algebra $A$ is strongly flat if for every real number $e $ there is a real number $0<s<e$ such that this deformation specialised at $t=s$ gives an algebra isomorphic to $A$. We show…
We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non-trivial elements in homotopy groups…
This paper is the second in a series dedicated to the operadic study of Nijenhuis structures, focusing on Nijenhuis Lie algebras and Nijenhuis geometry. We introduce the concept of homotopy Nijenhuis Lie algebras and establish that the…
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 complexes are quasi-isomorphic. Moreover, the result is extended to the…