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

Gareth Wilkes

doi:10.4171/ggd/569

JournalsggdVol. 14, No. 3pp. 917–948

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

Gareth Wilkes
University of Cambridge, UK

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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.

Cite this article

Gareth Wilkes, Classification of pro- $p$ PD $^{2}$ pairs and the pro- $p$ curve complex. Groups Geom. Dyn. 14 (2020), no. 3, pp. 917–948

DOI 10.4171/GGD/569