Stable existence of incompressible 3-manifolds in 4-manifolds

Qayum Khan; Gerrit Smith

doi:10.1016/j.topol.2019.04.006

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arXiv · 1702.05362

Stable existence of incompressible 3-manifolds in 4-manifolds

Qayum Khan·Gerrit Smith

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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.

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Qayum Khan, Gerrit Smith. 2017-02-17. Stable existence of incompressible 3-manifolds in 4-manifolds. https://doi.org/10.1016/j.topol.2019.04.006

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