Orbifolds as stacks
By Eugene Lerman. 2008
136 citations recorded by the source corpus.
The first goal of this survey paper is to argue that if orbifolds are groupoids, then the collection of orbifolds and their maps has to be thought of as a 2-category. Compare this with the classical definition of Satake and Thurston of orbifolds as a 1-category of sets with extra structure and/or with the "modern" definition of orbifolds as proper etale Lie groupoids up to Morita equivalence. The second goal is to describe two complementary ways of thinking of orbifolds as a 2-category: 1. the weak 2-category of foliation Lie groupoids, bibundles and equivariant maps between bibundles and 2. the strict 2-category of Deligne-Mumford stacks over the category of smooth manifolds.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/54ea056a5548ef7e81734e2398c739b915fd10c9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Central extensions of smooth 2–groups and a finite-dimensional string 2–group (2009, background): “e is also always of the form hfifor some functor f: X→Y. Hence if Xand Y are spaces the is the same as a map of spaces. If Xis an action groupoid, then this is just a G-invariant map. Proposition 23 ([Ler08]). A bibundle Pfrom Hto Gadmits a section of σ: P→H0 if and only if P∼=hfi for some smooth fu”