| Immersed and Virtually Embedded π1-Injective Surfaces in Graph Manifolds (2007) | |||||||||||||||
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| 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 1 -injective surface of negative Euler characteristic. We also determine the class of closed graph manifolds which have no nite cover containing an embedded such surface. This is a larger class. Thus, manifolds M 3 exist which have immersed 1 -injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (nitely covered by an embedded surface in some nite cover of M 3 ). AMS Classication 57M10, 57N10, 57R40, 57R42 Keywords 1 -injective surface, graph manifold, separable, surface subgroup 1 Introduction It is widely expected that any closed 3-manifold M 3 with innite fundamental group contains immersed 1 -injective surfaces. In fact, standard conjectures of Waldhausen, Thurston and ... | |||||||||||||||
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