Mathematics – Algebraic Topology
Scientific paper
2006-10-25
Mathematics
Algebraic Topology
36 pages, LaTeX. v2: Minor corrections, improvements in exposition
Scientific paper
Associated to any subspace arrangement is a "De Concini-Procesi model", a certain smooth compactification of its complement, which in the case of the braid arrangement produces the Deligne-Mumford compactification of the moduli space of genus 0 curves with marked points. In the present work, we calculate the integral homology of real De Concini-Procesi models, extending earlier work of Etingof, Henriques, Kamnitzer and the author on the (2-adic) integral cohomology of the real locus of the moduli space. To be precise, we show that the integral homology of a real De Concini-Procesi model is isomorphic modulo its 2-torsion with a sum of cohomology groups of subposets of the intersection lattice of the arrangement. As part of the proof, we construct a large family of natural maps between De Concini-Procesi models (generalizing the operad structure of moduli space), and determine the induced action on poset cohomology. In particular, this determines the ring structure of the cohomology of De Concini-Procesi models (modulo 2-torsion).
No associations
LandOfFree
The homology of real subspace arrangements 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 homology of real subspace arrangements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The homology of real subspace arrangements will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-378593