The General Notion of Descent in Coarse Geometry

Details The General Notion of Descent in Coarse Geometry The General Notion of Descent in Coarse Geometry

2010-02-24

arxiv.org/abs/1002.4563v1

Mathematics

Algebraic Topology

Scientific paper

In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological spaces there is an associated coarse assembly map from the topologically exicisive functor to the coarsely excisive functor. We conjecture that this coarse assembly map is an isomorphism for uniformly contractible spaces with bounded geometry, and show that the coarse isomorphism conjecture, along with some mild technical conditions, implies that a correspoding equivariant assembly map is injective. Particular instances of this equivariant assembly map are the maps in the Farrell-Jones conjecture, and in the Baum-Connes conjecture.

Affiliated with

Also associated with

No associations

Rating

The General Notion of Descent in Coarse Geometry 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 The General Notion of Descent in Coarse Geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The General Notion of Descent in Coarse Geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-260860