Submanifold Projection
Submanifold Projection
复制标题
子流形投影
DOI：
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复制
发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Savchuk
中科院分区：
文献类型：
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作者：
Lucas Sabalka;D. Savchuk
一个最有用的工具，研究几何的映射类组一直是地下投影的Masur和Minsky。在这里，我们提出了一个类似的研究的几何出（Fn）称为子流形投影。我们用二重体Mn = #S × S作为Fn的几何模型，考虑Mn中的本质嵌入2-球，其合痕类可以用自由群的自由分裂来识别.我们在球面复形（也称为分裂复形）的背景下解释子流形投影。我们证明了子流形投影满足一些理想的性质，包括Behrstock不等式和有界测地线像定理。我们对后者的证明依赖于一种方法，该方法将一个球体“相对于”另一个给定的球体进行规范化可视化，我们称之为球体树。球树与球的Hatcher范式有关，并且与Guirardel核的某些切片的解释一致。
One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky. Here we propose an analogue for the study of the geometry of Out(Fn) called submanifold projection. We use the doubled handlebody Mn = #S × S as a geometric model of Fn, and consider essential embedded 2-spheres in Mn, isotopy classes of which can be identified with free splittings of the free group. We interpret submanifold projection in the context of the sphere complex (also known as the splitting complex). We prove that submanifold projection satisfies a number of desirable properties, including a Behrstock inequality and a Bounded Geodesic Image theorem. Our proof of the latter relies on a method of canonically visualizing one sphere ‘with respect to’ another given sphere, which we call a sphere tree. Sphere trees are related to Hatcher normal form for spheres, and coincide with an interpretation of certain slices of a Guirardel core.
关于自由分裂和自由因子复合物的双曲性
DOI：
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发表时间：
2014
期刊：
and dynamics
影响因子：
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作者：
Kapovich, Ilya;Rafi, Kasra
通讯作者：
Rafi, Kasra