Related papers: On Local Integrability Conditions Of Jet Groupoids

In this talk the description of gauge theories associated with internal symmetries is extended to the case in which the symmetry group is the space-time translation group (recovering Einstein's theory) using the standard jet-bundle…

We address a natural question in noncommutative geometry, namely the rigidity observed in many examples, whereby noncommutative spaces (or equivalently their coordinate algebras) have very few automorphisms by comparison with their…

In this note we revisit the notions of transverse density bundle and of modular classes of Lie algebroids and Lie groupoids; in particular, we point out that one should use the transverse density bundle $\mathcal{D}_{A}^{\textrm{tr}}$…

This paper develops the tools of formal algebraic geometry in the setting of noncommutative manifolds, roughly ringed spaces locally modeled on the free associative algebra. We define a notion of noncommutative coordinate system, which is a…

A subcategory $\textbf{C}$ of a groupoid $\mathbb{G}$ is a left order in $\mathbb{G}$, if every element of $\mathbb{G}$ can be written as $a^{-1}b$ where $a, b \in \textbf{C}$. A subsemigroupoid $\mathfrak{C}$ of a groupoid $\mathbb{G}$ is…

In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive…

We characterize the triples (X,L,H), consisting of holomorphic line bundles L and H on a complex projective manifold X, such that for some positive integer k, the k-th holomorphic jet bundle of L, J_k(L), is isomorphic to a direct sum…

Semiclassical systems being symmetric under Lie group are studied. A state of a semiclassical system may be viewed as a set (X,f) of a classical state X and a quantum state f in the external classical background X. Therefore, the set of all…

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…

Let $\mathcal{J}^1$ be the real form of complex simple Jordan algebra with the automorphism group $G$ of type $F_{4(-20)}$. Explicitly, we give the orbit decomposition of $\mathcal{J}^1$ under the action of $G$ and determine the Lie group…

Let G be a Lie groupoid over M such that the target-source map from G to M x M is proper. We show that, if O is an orbit of finite type (i.e. which admits a proper function with finitely many critical points), then the restriction G|U of G…

We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators.

On a geometrically smooth complex algebraic curve X^1 in P^2(C), represented in complex affine coordinates (x,y) as the zero-locus R(x,y) = 0 of some polynomial R of degree d >= k+3, an explicit family of generating independent holomorphic…

Let E be a transitive Courant algebroid with scalar product of neutral signature. A generalized almost complex structure \mathcal J on E is a skew-symmetric smooth field of endomorphisms of E which squares to minus the identity. We say that…

Fix a point $t_0$ in the circle $S^1$. The space $J^k(t_0, \mathbb{P}^1)$ of $k$-jets at $t_0$ of $C^{\infty}$ maps from $S^1$ to the Riemann sphere $\mathbb{P}^1$ is a $k+1$ dimensional complex algebraic manifold. We identify a class of…

We introduce a new kind of groupoid--a pseudo \'etale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are…

It is well-known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. In other words, the fundamental groupoid functor can be…

In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a $W^*$-algebra. In particular the complex analytic manifold structure of these objects is investigated.…

Let $G$ be the group of orientation-preserving isometries of a rank-one symmetric space $X$ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $\Gamma \subset G$ on the boundary of $X$, which is…

We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a…