Immersed and virtually embedded pi_1-injective surfaces in graph manifolds

Details Immersed and virtually embedded pi_1-injective surfaces in graph manifolds Immersed and virtually embedded pi_1-injective surfaces in graph manifolds

1999-01-21

arxiv.org/abs/math/9901085v2

Algebr. Geom. Topol. 1 (2001) 411-426

Mathematics

Geometric Topology

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

Scientific paper

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).

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