منابع مشابه
Lengths of Systoles on Tileable Hyperbolic Surfaces
The same triangle may tile geometrically distinct surfaces of the same genus, and these tilings may determine isomorphic tiling groups. We determine if there are geometric differences in the surfaces that can be found using group theoretic methods. Specifically, we determine if the systole, the shortest closed geodesic on a surface, can distinguish a certain families of tilings. For example, th...
متن کاملSystoles of Arithmetic Hyperbolic Surfaces and 3–manifolds
Our main result is that for any positive real number x0, the set of commensurability classes of arithmetic hyperbolic 2– or 3–manifolds with fixed invariant trace field k and systole bounded below by x0 has density one within the set of all commensurability classes of arithmetic hyperbolic 2– or 3–manifolds with invariant trace field k. The proof relies upon bounds for the absolute logarithmic ...
متن کاملHomological Systoles, Homology Bases and Partitions of Riemann Surfaces
A compact Riemann surface of genus g, g > 1, can be decomposed into pairs of pants, i.e., into three hole spheres, by cutting the surface along 3g 3 simple closed non{intersecting geodesic curves. These curves can always be chosen in such a way that their hyperbolic lengths are bounded by 21g ([7]). First length controlled decompositions of Riemann surfaces into pairs of pants were found by Lip...
متن کاملSystoles and Intersystolic Inequalities
This articles surveys inequalities involving systoles in Riemannian geometry. Résumé. Cet article présente l’ensemble des inégalités connues sur les systoles en géométrie riemannienne. M.S.C. Subject Classification Index (1991) : 53C22. c © Séminaires & Congrès 1, SMF 1996
متن کاملSystoles of Hyperbolic 4-manifolds
We prove that for any ǫ > 0, there exists a closed hyperbolic 4manifold with a closed geodesic of length < ǫ.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06216-8