Realisation and Splitting for Poincaré Duality Pairs in Dimension Three
arXiv:2207.14054
Abstract
In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincaré duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are sufficient.
The construction for the main result doesn't work - there is a counter-example