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.
Maps vector fields between stacks and orbit spaces.
We introduce the notions of a differentiable groupoid and a differentiable stratified groupoid, generalizations of Lie groupoids in which the spaces of objects and arrows have the structures of differentiable spaces, respectively differentiable stratified spaces, compatible with the groupoid structure. After studying b…
We present some features of the smooth structure, and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures - it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object…
Establishes Morita equivalence for Nijenhuis structures and proves invariance of modular class.
New cohomology theory shows compact Lie group actions are Morita invariant.
Unified framework for Morita invariant cohomology of Lie groupoids.
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…
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.
Linearizability of singular foliations is preserved under a specific equivalence relation.
New Morita equivalence for diffeological groupoids defined.
Study of Morita equivalences in Lie groupoids and their symmetries.
In \cite{KOT:MORITA}, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds \HGF{7}{2}{}{8}$ is decomposed as a product of some leaf cohomology class and a transverse symplectic class . In other words, the Kontsevich homomorphism $\dsω\wedge :\HGF{5}{2}{0}{10} \rightarrow\HGF{7}{2}…
We prove the existence of Verdier stratifications for sets definable in any o-minimal structure on (R, +, .). It is also shown that the Verdier condition (w) implies the Whitney condition (b) in o-minimal structures on (R, +, .). As a consequence the Whitney Stratification Theorem holds. The existence of (wf)-stratific…
New models for symplectic structures on classifying stacks.
The paper studies HKKN stratifications for non-compact spaces and proves convexity properties.
Using Kontsevich's identification of the homology of the Lie algebra l_infty with the cohomology of Out(F_r), Morita defined a sequence of 4k-dimensional classes mu_k in the unstable rational homology of Out(F_{2k+2}). He showed by a computer calculation that the first of these is non-trivial, so coincides with the uni…
In this note we give geometric formulations and proofs of three results of S. Morita. These results relate certain two dimensional cohomology classes of various moduli spaces of curves. We also give a geometric interpretation of a fourth result of Morita. One motivation of this work is to facilitate the application of …
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…
Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus with one boundary component to , the third exterior product of the homology of the surface. Morita then extended Johnson's homomorphism to a homomorphism from the entire mapping cla…
New bridge between diffeology and noncommutative geometry.
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…
In this work we prove a residue formula for Morita-Futaki-Bott invariant with respect any holomorphic vector fields with isolated (possibly degenerated) singularities in terms of Grothendieck's residues.
Stratifies representation varieties of twisted Hopf links.
The paper defines a stratification for Lie groupoids in a tame topology context.
Paper confirms MCS spaces are equivalent to CS sets.
Alexandrov spaces have a special stratification that maps to spheres.
In this note we study the localization of Futaki-Morita integrals at isolated degenerate zeros by giving a streamlined exposition in the spirit of Bott and implement the localization procedure for a holomorphic vector field on with a maximally degenerate zero, giving an essentially unique formula for the Futaki-…
We obtain a combinatorial formula for the Miller-Morita-Mumford classes for the mapping class group of punctured surfaces and prove Witten's conjecture that they are proportional to the dual to the Witten cycles. The proportionality constant is shown to be exactly as conjectured by Arbarello and Cornalba [J. Alg. Geom.…
Investigates properties of moment maps and stratifications on Lie groups.
Solves open problem on Lie groupoids equivalence.
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…
Optimizes biharmonic map regularity using stratification methods.
New stratification reveals intrinsic singularity types of orbit spaces.
Proposes a topological framework to study modular invariants and related concepts.
We extend certain homomorphisms defined on the higher Torelli subgroups of the mapping class group to crossed homomorphisms defined on the entire mapping class group. In particular, for every , we construct a crossed homomorphism which extends Morita's homomorphism to the entire mapping clas…
The aim of this paper is to compare stratifications of moduli spaces given by group actions in the case of similarity of matrices introduced by Arnold and the author's stratification by projective orbifolds, and its relation to deformations o elements in the moduli space.
Combines k-means and hill climbing for stratification and allocation.
Social media enhances or diminishes scientific status, depending on usage.
Abstract: Bijection strengthened to Morita equivalence integrating Poisson and Cartan-Dirac structures.
We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.
We answer a question posed by Morita concerning the non-triviality of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism groups in homology of small degree.
Study mapping class groups and their representations linking to algebraic structures.
Study clarifies variance of stratification estimators for causal effects.
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)-…
In this article, we define and study the total Milnor invariant and the infinitesimal Morita-Milnor homomorphism as punctured disk analogues of the total Johnson map and the infinitesimal Morita homomorphism studied by Kawazumi and Massuyeau in the case of surface of positive genus with one boundary component.
In this paper, we generalize the notion of Serre fibration to the Morita category of topological groupoids and derive the associated long exact sequence of homotopy groups. We use this results for calculation of homotopy groups of various groupoids, such as the foliation groupoid of a Riemannian foliation.
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…