Related papers: Normed groupoids with dilations
Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with $\delta$-structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric…
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several…
We study several aspects of the regular deformations of completely integrable systems. Namely, we prove the existence of a Hamiltonian normal form for these deformations and we show the necessary and sufficient conditions a perturbation has…
We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…
We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
We study deformations of the discrete Heisenberg group acting properly discontinuously on the Heisenberg group from the left and right and obtain a complete description of the deformation space.
We will define and study (moduli) spaces of deformations of irregular classes on Riemann surfaces, which provide an intrinsic viewpoint on the `times' of irregular isomonodromy systems in general. Our aim is to study the deeper…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
Boundary groupoids were introduced by the second author, which can be used to model many analysis problems on singular spaces. In order to investigate index theory on boundary groupoids, we introduce the notion of {\em a deformation from…
We develop the deformation theory of A_\infty algebras together with \infty inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A_\infty…
We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using multiderivations of hom-Lie-Rinehart algebras.
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…
In this paper we present a geometrical framework to study the uniformity of a composite material by means of double groupoid theory. The notions of vertical and horizontal uniformity are introduced, as well as other weaker ones that allows…
In the spirit of Conway we define a groupoid starting from projective planes of order $q$, where $q$ is odd. The associated group of these groupoids is then investigated.
We describe the deformation cohomology of a symplectic groupoid, and use it to study deformations via Moser path methods, proving a symplectic groupoid version of the Moser Theorem. Our construction uses the deformation cohomologies of Lie…