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2001 Immersed and virtually embedded $\pi_1$–injective surfaces in graph manifolds
Walter D Neumann
Algebr. Geom. Topol. 1(1): 411-426 (2001). DOI: 10.2140/agt.2001.1.411

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 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).

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Walter D Neumann. "Immersed and virtually embedded $\pi_1$–injective surfaces in graph manifolds." Algebr. Geom. Topol. 1 (1) 411 - 426, 2001. https://doi.org/10.2140/agt.2001.1.411

Information

Received: 27 March 2001; Accepted: 6 July 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0979.57007
MathSciNet: MR1852764
Digital Object Identifier: 10.2140/agt.2001.1.411

Subjects:
Primary: 57M10
Secondary: 57N10, 57R40, 57R42

Rights: Copyright © 2001 Mathematical Sciences Publishers

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