منابع مشابه
Compressing totally geodesic surfaces
In this paper we prove that one can find surgeries arbitrarily close to infinity in the Dehn surgery space of the figure eight knot complement for which some immersed totally geodesic surface compresses. MSC: 57M25, 57M50
متن کاملTotally geodesic surfaces and homology
We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.
متن کاملHyperbolic Knot Complements without Closed Embedded Totally Geodesic Surfaces
It is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces can ...
متن کاملProving the absence of certain totally geodesic surfaces
We have proven the absence of totally geodesic surfaces bounded or punctured by either the figure-eight knot or the 62 link. We’ve also found a case (Borromean Rings checkerboard) in which a Dehn filling changes a surface that is not totally geodesic into one that is.
متن کاملTotally Geodesic Submanifolds of Teichmüller Space
Main results. Let Tg,n andMg,n denote the Teichmüller and moduli space respectively of genus g Riemann surfaces with n marked points. The Teichmüller metric on these spaces is a natural Finsler metric that quantifies the failure of two different Riemann surfaces to be conformally equivalent. It is equal to the Kobayashi metric [Roy74], and hence reflects the intrinsic complex geometry of these ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2002
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(01)00029-3