Stable existence of incompressible 3-manifolds in 4-manifolds
arXiv:1702.05362 · doi:10.1016/j.topol.2019.04.006
Abstract
Given an injective amalgam at the level of fundamental groups and a specific 3-manifold, is there a corresponding geometric-topological decomposition of a given 4-manifold, in a stable sense? We find an algebraic-topological splitting criterion in terms of the orientation classes and universal covers. Also, we equivariantly generalize the Lickorish--Wallace theorem to regular covers.
13 pages; Version 3: revised introduction and added references; accepted by Topology and its Applications