Counting essential surfacesin a closed hyperbolic three-manifold
نویسندگان
چکیده
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 improves on the work by Masters.
منابع مشابه
October 26, 2011 COUNTING ESSENTIAL SURFACES IN A CLOSED HYPERBOLIC THREE MANIFOLD
Let M be a closed hyperbolic three manifold. We show that the number of genus g surface subgroups of π1(M ) grows like g.
متن کاملNoncompact Fuchsian and quasi-Fuchsian surfacesin hyperbolic 3--manifolds
Given a noncompact quasi-Fuchsian surface in a finite volume hyperbolic 3–manifold, we introduce a new invariant called the cusp thickness, that measures how far the surface is from being totally geodesic. We relate this new invariant to the width of a surface, which allows us to extend and generalize results known for totally geodesic surfaces. We also show that checkerboard surfaces provide e...
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 کاملOrbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملImmersing 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 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 2012