Homotopy Theory of Orbispaces

Details Homotopy Theory of Orbispaces Homotopy Theory of Orbispaces

2007-01-31

arxiv.org/abs/math/0701916v1

Mathematics

Algebraic Topology

52 pages

Scientific paper

Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the category of contravariant functors Func(Orb_G,Spaces) have equivalent homotopy theories. We extend this result to the context of orbispaces, with the role of Orb_G now played by a category whose objects are topological groups and whose morphisms are given by Hom(H,G) = Mono(H,G) x_G EG. On our way, we endow the category of topological groupoids with notions of weak equivalence, fibrant objects, and cofibrant objects, and show that it then shares many of the properties of a Quillen model category.

Affiliated with

Also associated with

No associations

Rating

Homotopy Theory of Orbispaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homotopy Theory of Orbispaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homotopy Theory of Orbispaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-457327