A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Establishes Morita equivalence for Nijenhuis structures and proves invariance of modular class.
Linearizability of singular foliations is preserved under a specific equivalence relation.
Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of -algebras over a ring $\ring C$ which is the quadratic extension by $\im$ of an ordered ring $\ring R$. The goal of the present paper is twofold. First, we clarify the relationship betw…
Proof that m-shifted symplectic forms are preserved under Morita equivalence of Lie n-groupoids.
New Morita equivalence for diffeological groupoids defined.
Study of Morita equivalences in Lie groupoids and their symmetries.
These notes discuss various aspect of the ``representation theory'' of Poisson manifolds, with focus on Morita equivalence and Picard groups. We give a brief introduction to Poisson geometry (including Dirac and twisted Poisson structures) and algebraic Morita theory before presenting the geometric Morita theory of Poi…
New models for symplectic structures on classifying stacks.
We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent in…
Solves open problem on Lie groupoids equivalence.
Let be a finite group. Noncommutative geometry of unital -algebras is studied. A geometric structure is determined by a spectral triple on the crossed product algebra associated with the group action. This structure is to be viewed as a representative of a noncommutative orbifold. Based on a study of classical o…
New bridge between diffeology and noncommutative geometry.
Abstract: Bijection strengthened to Morita equivalence integrating Poisson and Cartan-Dirac structures.
An orbifold is a Morita equivalence class of a proper {\' e}tale Lie groupoid. A unitary equivalence class of spectral triples over the algebra of smooth invariant functions are associated with any compact spin orbifold. In the case of an effective spin orbifold we construct a collection of spectral triples over the sm…
A nice differential-geometric framework for (non-abelian) higher gauge theory is provided by principal 2-bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local trivializations are kinds of Morita equivalences, and connections are Lie-2-algebra-valued 1-forms. In this article, we const…
New cohomology theory shows compact Lie group actions are Morita invariant.
The paper introduces SRFs and I-Poisson manifolds, linking foliations to Riemannian geometry.
We introduce a weak concept of Morita equivalence, in the birational context, for Poisson modules on complex normal Poisson projective varieties. We show that Poisson modules, on projective varieties with mild singularities, are either rationally Morita equivalent to a flat partial holomorphic sheaf, or a sheaf with a …
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The s…
Any etale Lie groupoid G is completely determined by its associated convolution algebra C_c(G) equipped with the natural Hopf algebroid structure. We extend this result to the generalized morphisms between etale Lie groupoids: we show that any principal H-bundle P over G is uniquely determined by the associated C_c(G)-…
Undecidability proved for DG algebras problems.
New construction of Turaev-Viro invariants invariant under Morita equivalence.
Introduces a new equivalence for singular foliations and their groupoids.
An arbitrary Lie groupoid gives rise to a groupoid of germs of local diffeomorphisms over its base manifold, known as its effect. The effect of any bundle of Lie groups is trivial. All quotients of a given Lie groupoid determine the same effect. It is natural to regard the effects of any two Morita equivalent Lie group…
We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that characterizes VB-Morita maps in terms of fiber and basic data, and use it to prove the Morita invariance of VB-cohomology, with implications to defor…
A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary algebroids. Basic properties of the Poisson K-ring are proved and the Poisson K-rings are calcul…
New concept of coisotropic structures for differentiable stacks defined.
This paper proves cohomology invariants for differentiable stacks.
Defines basic sections of LA-groupoids for simpler modeling.
Lie groupoids and their orbit spaces are linked through equivalence classes.
The purpose of this paper is to investigate shifted Poisson structures in context of differential geometry. The relevant notion is shifted Poisson structures on differentiable stacks. More precisely, we develop the notion of Morita equivalence of quasi-Poisson groupoids. Thus isomorphism classes of …
We compute the Picard group of a stable b-symplectic manifold by introducing a collection of discrete invariants which classify up to Morita equivalence.
This is a condensed exposition of the results of a future work, based on a talk of the second author at the Oberwolfach workshop "Poisson Geometry", April 30--4 May 2007.
We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kähler structure of symplectic type. For a usual Kähler structure, it is well-known that the geometry is determined by a complex structure, a Kähler class, and the choice of a positive -form in this class, which depen…
Functor connects sheaves on Lagrangian cobordisms, proving equivalence and action decreasing properties.
We introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of Androulidakis-Skandalis. We show that our notion of equivalence is compatible wi…
We consider principal bundles as generalized morphisms between topological groupoids. In the category of these generalized morphisms two topological groupoids are isomorphic if and only if they are Morita equivalent. We show that the fibers of a generalized morphism from H to G induce a singular foliation of the topolo…
Let be a Lie algebroid. In this short note, we prove that a pull-back of along a fibration with homologically -connected fibers, shares the same deformation cohomology of up to degree .
This research reinterprets Lie and Cartan's work on geometric structures using Lie groupoids.
Study logarithmic flat connections on principal bundles using Lie groupoids.
The paper constructs a symplectic groupoid for a specific Poisson structure.
We discuss two sorts of generalization of Lie groupoids. One is Lie -groupoids defined as simplicial manifolds with trivial . The other is the stacky Lie groupoid $\cG\rra M$ with $\cG$ a differentiable stack. We build 1-1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain…
This paper connects geometric diagrams to spherical T-duality.
Extends connections on Lie groupoids, proving completeness conditions.
In this paper we study the Lie groupoids which appear in foliation theory. A foliation groupoid is a Lie groupoid which integrates a foliation, or, equivalently, whose anchor map is injective. The first theorem shows that, for a Lie groupoid G, the following are equivalent: - G is a foliation groupoid, - G has discrete…
Study of generalized double Bruhat cells and their integrations.
The aim of this paper is to review and discuss in detail local aspects of principal bundles with groupoid structure. Many results, in particular from the second and third section, are already known to some extents, but, due to the lack of a ``unified'' point of view on the subject, I decided nonetheless to (re)define a…
Generalizes van Est map to geometric stacks and homotopy theory.