Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 1, Number 1 (2001), 411-426.
Immersed and virtually embedded $\pi_1$–injective surfaces in graph manifolds
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 –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 exist which have immersed –injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (finitely covered by an embedded surface in some finite cover of ).
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 411-426.
Received: 27 March 2001
Accepted: 6 July 2001
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M10: Covering spaces
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57R40: Embeddings 57R42: Immersions
Neumann, Walter D. Immersed and virtually embedded $\pi_1$–injective surfaces in graph manifolds. Algebr. Geom. Topol. 1 (2001), no. 1, 411--426. doi:10.2140/agt.2001.1.411. https://projecteuclid.org/euclid.agt/1513882600