Related papers: Reduced smooth stacks?

Let G be a (not necessarily Hausdorff) locally compact groupoid. We introduce a notion of properness for G, which is invariant under Morita-equivalence. We show that any generalized morphism between two locally compact groupoids which…

Let M be a homogeneous space admitting a left translation by a connected Lie group G. The adjoint to the action gives rise to a map from G to the monoid of self-homotopy equivalences of M.The purpose of this paper is to investigate the…

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized $F$-structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized…

We develop a theory of Lie algebroids over differentiable stacks that extends the standard theory of Lie algebroids over manifolds. In particular we show that Lie algebroids satisfy descent for submersions, define the category of Lie…

We show that the complete bornological convolution algebras of Lie groupoids and convolution bimodules of groupoid bibundles define a monoidal functor from the 2-category of differentiable stacks to the Morita 2-category of complete…

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,…

The author provides some definitions and structural results about Fell bundles, defined as C^*-algebra bundles over topological groupoids. Such bundles are a mutual generalization of semi-direct products of groups with C^*-algebras and…

We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…

In this PhD thesis, we have studied certain geometric structures over Lie groupoids and differentiable stacks. This thesis is based on the work [arXiv:2103.04560, arXiv:2012.08447, arXiv:2012.08442, arXiv:1907.00375]. In [arXiv:1907.00375],…

Various aspects of Morita theory of deformed algebras and in particular of star product algebras on general Poisson manifolds are discussed. We relate the three flavours ring-theoretic Morita equivalence, $^*$-Morita equivalence, and strong…

Given a derived equivalence of orbifolds associated to projective varieties with (not necessarily Gorenstein) quotient singularities, we deduce consequences related to the behavior of orbifold Hodge numbers and the Picard variety, extending…

Due to a result by Mackenzie, extensions of transitive Lie groupoids are equivalent to certain Lie groupoids which admit an action of a Lie group. This paper is a treatment of the equivariant connection theory and holonomy of such…

This is a preliminary version of a book on infinite-dimensional Lie groups. It covers the basics of calculus and manifolds in the context of locally convex spaces, based on Bastiani's notion of a smooth map. Starting from this concept, we…

This unpublished note contains some materials taken from my old study note on groupoids and small categories. It contains a proof for the fact that any groupoid is a group bundle over an equivalence relation. Moreover, the action of a…

By results of the second author, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived…

We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…

For a Lie group G and a smooth manifold W, we study the difference between smooth actions of G on W and bundles over the classifying space of G with fiber W and structure group Diff(W). In particular, we exhibit smooth manifold bundles over…

Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general…

We show that any proper Lie groupoid admits a compatible (real) analytic structure.