Covering Homology

Details Covering Homology Covering Homology

2007-06-05

arxiv.org/abs/0706.0626v2

Mathematics

Algebraic Topology

32 pages

Scientific paper

We introduce the notion of "covering homology" of a commutative ring spectrum with respect to certain families of coverings of topological spaces. The construction of covering homology is extracted from Bokstedt, Hsiang and Madsen's topological cyclic homology. In fact covering homology with respect to the family of orientation preserving isogenies of the circle is equal to topological cyclic homology. Our basic tool for the analysis of covering homology is a cofibration sequence involving homotopy orbits and a restriction map similar to the restriction map used in Bokstedt, Hsiang and Madsen's construction of topological cyclic homology. Covering homology with respect to families of isogenies of a torus is constructed from iterated topological Hochschild homology. It receives a trace map from iterated algebraic K-theory and the hope is that the rich structure, and the calculability of covering homology will make covering homology useful in the exploration of J. Rognes' ``red shift conjecture''.

Affiliated with

Also associated with

No associations

Rating

Covering Homology 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 Covering Homology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Covering Homology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-122178