منابع مشابه
The geometry of purely loxodromic subgroups of right-angled Artin groups
We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group A(Γ) fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups Mod(S). In particular, such subgroups are quasiconvex in A(Γ). In addition, we identify a milder condition for a finitely generated subgroup of A(Γ) that guarantees it is free, undistorted, a...
متن کاملAll discrete RP groups with non-π-loxodromic generators
In this paper we give necessary and sufficient conditions for discreteness of a group generated by a hyperbolic element and an elliptic one of odd order with intersecting axes. This completes classification of the discrete groups with non-π-loxodromic generators in the class of twogenerator groups with real parameters. The criterion is given also as a list of all parameters that correspond to d...
متن کاملLoxodromic Spirals in M. C. Escher's Sphere Surface
Loxodromic spirals are the analogues in spherical geometry of logarithmic spirals on the plane. M.C. Escher’s 1958 woodcut Sphere Surface is an image of black and white fish arranged along eight spiral paths on the surface of a sphere. By connecting the plane and spherical models of the complex numbers, we show that Sphere Surface is the conformal image on the sphere of a tessellation of fish o...
متن کاملLoxodromic Elements in the Cyclic Splitting Complex and Their Centralizers
We show that an outer automorphism acts loxodromically on the cyclic splitting complex if and only if it has a filling lamination and no generic leaf of the lamination is carried by a vertex group of a cyclic splitting. This is the analog for the cyclic splitting complex of HandelMosher’s theorem on loxodromics for the free splitting complex. We also show that such outer automorphisms have virt...
متن کاملOpen Sets of Maximal Dimension in Complex Hyperbolic Quasi-fuchsian Space
Let π1 be the fundamental group of a closed surface Σ of genus g > 1. One of the fundamental problems in complex hyperbolic geometry is to find all discrete, faithful, geometrically finite and purely loxodromic representations of π1 into SU(2, 1), (the triple cover of) the group of holomorphic isometries of H2C. In particular, given a discrete, faithful, geometrically finite and purely loxodrom...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1936
ISSN: 1802-114X
DOI: 10.21136/cpmf.1936.123697