Algebraic and Geometric Topology 1 (2001),
paper no. 20, pages 411-426.
Immersed and virtually embedded pi_1-injective surfaces in graph manifolds
Walter D. Neumann
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).
Keywords.
pi_1-injective surface, graph manifold, separable, surface subgroup
AMS subject classification.
Primary: 57M10.
Secondary: 57N10, 57R40, 57R42.
DOI: 10.2140/agt.2001.1.411
E-print: arXiv:math.GT/9901085
Submitted: 27 March 2001.
Accepted: 6 July 2001.
Published: 9 July 2001.
Notes on file formats
Walter D. Neumann
Department of Mathematics, Barnard College, Columbia University
New York, NY 10027, USA
Email: neumann@math.columbia.edu
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