2016/03/14 by Pierre Albin, Albin, Pierre · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1603.04106
This article is a survey of recent work of the author, together with Markus Banagl, Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza, on the Hodge theory of stratified spaces. We discuss how to resolve a Thom-Mather stratified space to a manifold with corners with an iterated fibration structure and the generalization of a perversity in the sense of Goresky-MacPherson to a mezzoperversity. We define Cheeger spaces and their signatures and describe how to carry out the analytic proof of the Novikov conjecture on these spaces. Finally we review the reductive Borel-Serre compactification of a locally symmetric space to a stratified space and describe its resolution to a manifold with corners.