Haken 3-Manifolds in Small Covers

Abstract

The authors prove that a 3-dimensional small cover M is a Haken manifold if and only if M is aspherical or equivalently the underlying simple polytope is a flag polytope. In addition, they find that M being Haken is also equivalent to the existence of a Riemannian metric with non-positive sectional curvature on M.

Keywords

Small cover / Haken manifold / Incompressible surface / Flag polytope

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