Immersed and virtually embedded pi_1-injective surfaces in graph manifolds
摘要
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).
引用
@article{arxiv.math/9901085,
title = {Immersed and virtually embedded pi_1-injective surfaces in graph manifolds},
author = {Walter D. Neumann},
journal= {arXiv preprint arXiv:math/9901085},
year = {2014}
}
备注
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-20.abs.html