论文标题
表面映射类组的扭曲 - 金属拓扑
The twist-cofinite topology on the mapping class group of a surface
论文作者
论文摘要
在紧凑连接的定向表面的映射类组上定义了拓扑。结果表明，映射类组的子集的“通用性”概念来自此定义。这个概念很容易得出许多合理的结果。例如，伪anosov图的集合被证明是通用的，可以假定具有任意的大拉伸因子。令M为从固定属G和通用胶水图的Heegaard分裂获得的3个manifold。结果表明，对于这样的歧管，通常m是双曲线，首先具有betti数为零，而Heegaard属完全等于g。
A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this notion easily; for example, the set of pseudo-Anosov maps is shown to be generic, and can be assumed to have arbitrary large stretch factor, generically. Let M be a 3-manifold obtained from a Heegaard splitting of fixed genus g and generic gluing map. It is shown that for such manifolds, generically M is hyperbolic, has first Betti number zero and Heegaard genus exactly equal to g.
