Immersed and virtually embedded pi_1-injective surfaces in graph manifolds

Abstract

We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed pi_1-injective surface of negative Euler characteristic. We also determine the class of closed graph manifolds which have no finite cover containing an embedded such surface. This is a larger class. Thus, manifolds M^3 exist which have immersed pi_1-injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (finitely covered by an embedded surface in some finite cover of M^3).

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-20.abs.html

References in corpus (2)

• 3-manifolds with(out) metrics of nonpositive curvature
• Immersed and virtually embedded pi_1-injective surfaces in graph manifolds

Cited by in corpus (6)

• Surface groups are flexibly stable
• Immersed and virtually embedded pi_1-injective surfaces in graph manifolds
• Simplicial volume of one-relator groups and stable commutator length
• Distortion of surfaces in graph manifolds
• A characterization of virtually embedded subsurfaces in 3-manifolds
• Topological and geometric properties of graph-manifolds