Geodesic
Immersed and virtually embedded π1–injective surfaces in graph manifolds
Neumann, Walter D1
1Department of Mathematics, Barnard College, Columbia University, New York NY 10027, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 411-426
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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 π1–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 M3 exist which have immersed π1–injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (finitely covered by an embedded surface in some finite cover of M3).

DOI : 10.2140/agt.2001.1.411
Keywords: $\pi_1$-injective surface, graph manifold, separable, surface subgroup

Neumann, Walter D  1

1 Department of Mathematics, Barnard College, Columbia University, New York NY 10027, USA 
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Neumann, Walter D. Immersed and virtually embedded π1–injective surfaces in graph manifolds. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 411-426. doi: 10.2140/agt.2001.1.411

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