Mathematics – Algebraic Topology
Scientific paper
2010-07-22
Mathematics
Algebraic Topology
44 pages. This final version will appear in Documenta Mathematica. Remark 8.23 has been improved, discussion of Grothendieck c
Scientific paper
In a previous article, we introduced notions of finiteness obstruction, Euler characteristic, and L^2-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homotopy colimits of I-indexed categories where I is any small category admitting a finite I-CW-model for its I-classifying space. Special cases of our Homotopy Colimit Formula include formulas for products, homotopy pushouts, homotopy orbits, and transport groupoids. We also apply our formulas to Haefliger complexes of groups, which extend Bass--Serre graphs of groups to higher dimensions. In particular, we obtain necessary conditions for developability of a finite complex of groups from an action of a finite group on a finite category without loops.
Fiore Thomas M.
Lück Wolfgang
Sauer Roman
No associations
LandOfFree
Euler Characteristics of Categories and Homotopy Colimits 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 Euler Characteristics of Categories and Homotopy Colimits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Euler Characteristics of Categories and Homotopy Colimits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-612379