October 26, 2011 COUNTING ESSENTIAL SURFACES IN A CLOSED HYPERBOLIC THREE MANIFOLD
نویسندگان
چکیده
Let M be a closed hyperbolic three manifold. We show that the number of genus g surface subgroups of π1(M ) grows like g.
منابع مشابه
Immersing almost geodesic surfaces in a closed hyperbolic three manifold
Let M be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into M so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.
متن کاملCounting essential surfacesin a closed hyperbolic three-manifold
Recently, we showed [3] that every closed hyperbolic 3–manifold M contains an essential subsurface and consequently 1.M/ contains a surface subgroup. It is therefore natural to consider the question: How many conjugacy classes of surface subgroups of genus g there are in 1.M/? This has already been considered by Masters [5], and our approach to this question builds on our previous work and impr...
متن کاملAsymptotics of the Length Spectrum for Hyperbolic Manifolds of Infinite Volume
We compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and nite-volume surfaces to this class of in nite-volume hyperbolic manifolds.
متن کاملSurfaces in Three-manifolds with Hyperbolic Fundamental Group
We show that if a closed irreducible three-manifold with hyperbolic fundamental group contains a surface subgroup satisfying a certain geometric regularity assumption, then the surface is either quasiconvex or a virtual fiber. In the latter case, the manifold is hyperbolic. The regularity condition ensures that we may find algebraic bounds on the surface group which are analogous to the diamete...
متن کاملDehn filling of cusped hyperbolic 3-manifolds with geodesic boundary
We define for each g > 2 and k > 0 a set Mg,k of orientable hyperbolic 3manifolds with k toric cusps and a connected totally geodesic boundary of genus g. Manifolds in Mg,k have Matveev complexity g+k and Heegaard genus g+1, and their homology, volume, and Turaev-Viro invariants depend only on g and k. In addition, they do not contain closed essential surfaces. The cardinality of Mg,k for a fix...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011