Classification of pro-$p$ PD$^2$ pairs and the pro-$p$ curve complex
Gareth Wilkes
TL;DR
This paper classifies pro-$p$ Poincaré duality pairs in dimension two, constructs a pro-$p$ analogue of the curve complex, and explores related properties of the mapping class group.
Contribution
It provides a classification of pro-$p$ Poincaré duality pairs and introduces a new pro-$p$ curve complex with foundational properties.
Findings
Classification of pro-$p$ Poincaré duality pairs in dimension two
Construction of a pro-$p$ curve complex
Results on separability properties of the mapping class group
Abstract
We classify pro- Poincar\'e duality pairs in dimension two. We then use this classification to build a pro- analogue of the curve complex and establish its basic properties. We conclude with some statements concerning separability properties of the mapping class group.
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