Heegaard Splittings and Pseudo-Anosov Maps
Heegaard Splittings and Pseudo-Anosov Maps
复制标题
Heegaard 分裂和伪阿诺索夫映射
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Souto
中科院分区：
文献类型：
--
作者：
Hossein Namazi;J. Souto
给定两个3维流形体，它们的边界与亏格g > 1的曲面S相同，并且具有不同的方向，我们考虑通过S的“一般”伪Anosov同胚f的迭代fn胶合这些流形体得到的流形序列Mn.利用开双曲三维流形上双曲结构的形变理论，当n足够大时，我们在Mn上构造了一个负曲度量，其中截面曲率在一个以-1为中心的给定小区间内收缩.这个构造足够具体，使我们能够描述这些流形的几何极限，因为n趋于无穷大，度量更接近于双曲。这样的描述使我们能够证明各种拓扑和群论性质的Mn，为n足够大，这将是不可用的知道仅仅存在一个负弯曲，甚至双曲度量Mn。
Given two 3-dimensional handlebodies whose boundaries are identified with a surface S of genus g > 1 and with different orientations, we consider the sequence of manifolds Mn obtained by gluing the handlebodies via the iteration fn of a “generic” pseudo-Anosov homeomorphism f of S. Using the deformation theory of hyperbolic structures on open hyperbolic 3-manifolds and for n sufficiently large, we construct a negatively curved metric on Mn where the sectional curvatures are pinched in a given small interval centered at –1. The construction is concrete enough to allow us describe the geometric limits of these manifolds as n tends to infinity and the metrics get closer to being hyperbolic. Such a description allows us to prove various topological and group theoretical properties of Mn, for n sufficiently large, which would not be available knowing the mere existence of a negatively curved or even hyperbolic metric on Mn.