Classification of pro-$p$ PD${}^2$ pairs and the pro-$p$ curve complex

Abstract

We classify pro-$p$ Poincaré duality pairs in dimension two. We then use this classification to build a pro-$p$ analogue of the curve complex and establish its basic properties. We conclude with some statements concerning separability properties of the mapping class group.

arXiv comment27 pages. Updated with some minor corrections; Section 5 added