Realisation and Splitting for Poincar\'e Duality Pairs in Dimension Three

TL;DR

This paper establishes that the necessary conditions previously identified for 3-dimensional Poincaré duality pairs with aspherical boundary components are also sufficient, through a new constructive approach.

Contribution

It provides a construction demonstrating that the necessary conditions for such duality pairs are also sufficient, completing the characterization.

Findings

Necessary conditions are sufficient for 3D Poincaré duality pairs.

Constructive method confirms the completeness of these conditions.

Advances understanding of the topology of 3D Poincaré duality pairs.

Abstract

In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincar\'e duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are sufficient.