Related papers: Atlases for Ineffective Orbifolds
This is a concise introduction to the theory of Lie groupoids, with emphasis in their role as models for stacks. After some preliminaries, we review the foundations on Lie groupoids, and we carefully study equivalences and proper groupoids.…
In this note we classify simply connected rationally elliptic compact toric orbifolds up to algebraic isomorphism.
We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces,…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…
This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.
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.…
We construct new invariants of equivariant birational isomorphisms taking values in equivariant Burnside groups.
We endow the diffeomorphism group of a paracompact (reduced) orbifold with the structure of an infinite dimensional Lie group modelled on the space of compactly supported sections of the tangent orbibundle. For a second countable orbifold,…
A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold that is locally modeled on $R^n$ modulo the action of a finite group. Orbifolds have proven interesting in a variety of settings. Spectral geometers have…
We define the Deligne Mumford orbifold axiomatically by a universal mapping property, show that this universal mapping property is equivalent to an infinitessimal universal mapping property, and use the latter to give an existence proof.
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…
The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
Using equivariant obstruction theory we construct equivariant maps from certain classifying spaces to representation spheres for cyclic groups, product of elementary Abelian groups and dihedral groups. Restricting them to finite skeleta…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
A common criticism of infinity-categories in algebraic geometry is that they are an extremely technical subject, so abstract to be useless in everyday mathematics. The aim of this note is to show in a classical example that quite the…
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…