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).Comment: 36 pages, LaTeX. v2: Minor corrections, improvements in expositio
