图流形中的浸入和虚嵌入pi_1-内射曲面
Immersed and virtually embedded pi_1-injective surfaces in graph manifolds
摘要：
我们证明了许多3-流形群没有非交换曲面子群。例如，孤立复曲面奇点的任何环节都具有这种性质。实际上，我们确定了不具有负欧拉示性数的浸入pi_1-内射曲面的闭图流形的确切类。我们还确定了一类闭图流形，没有有限覆盖包含嵌入这样的表面。这是一个更大的类。因此，存在流形M^3，它具有负欧拉示性数的浸入pi_1-内射曲面，但没有这样的曲面是虚嵌入的（被M^3的某个有限覆盖中的嵌入曲面所覆盖）。
英文摘要：
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).
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