Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbispaces and Orbifolds from the Point of View of the Borel
  Construction, a new Definition   ``An orbifold is a space which is locally modeled on the quotient of a vector
space by a finite group.'' This sentence is so easily said or written that more
than one person has missed some of the subtleties hidden by orbifolds.
Orbifolds were first introduced by Satake under the name ``V-manifold'' and
rediscovered by Thurston who called them ``orbifolds''. Both of them used only
faithful actions to define their orbifolds (these are the so called reduced
orbifolds). This intuitive restriction is very unnatural mathematically if we
want for example to study suborbifolds. Orbispaces are to topological spaces
what orbifolds are to manifolds. They have been defined by Haefliger via
topological groupoids. He defined the homotopy and (co)homology groups of an
orbispace to be those of the classifying space of the topological groupoid.
However, his definition of morphisms is complicated and technical. Ruan and
Chen have tried to reformulate the definitions, but they don't seem treat the
non-reduced case in a satisfactory way. Our idea is to define orbispaces and
orbifolds directly via their classifying spaces. This approach allows us to
easily define morphisms of orbispaces and orbifolds with all the desired good
properties.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph