منابع مشابه
Hyperbolic Triangular Buildings Without Periodic Planes of Genus 2
We study surface subgroups of groups acting simply transitively on vertex sets of certain hyperbolic triangular buildings. The study is motivated by Gromov’s famous surface subgroup question: Does every oneended hyperbolic group contain a subgroup which is isomorphic to the fundamental group of a closed surface of genus at least 2? In [10] and [3] the authors constructed and classified all grou...
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This survey is intended as a brief introduction to the theory of hyperbolic buildings and their lattices. Hyperbolic buildings are negatively curved geometric objects which also have a rich algebraic and combinatorial structure, and the study of these buildings and the lattices in their automorphism groups involves a fascinating mixture of techniques from many different areas of mathematics. Ro...
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We characterize the volume entropy of a regular building as the topological pressure of the geodesic flow on an apartment. We show that the entropy maximizing measure is not Liouville measure for any regular hyperbolic building. As a consequence, we obtain a strict lower bound on the volume entropy in terms of the branching numbers and the volume of the boundary polyhedrons.
متن کاملSurface Quotients of Hyperbolic Buildings
Let Ip,v be Bourdon’s building, the unique simply connected 2-complex such that all 2-cells are regular right-angled hyperbolic p-gons and the link at each vertex is the complete bipartite graph Kv,v. We investigate and mostly determine the set of triples (p, v, g) for which there exists a uniform lattice Γ = Γp,v,g in Aut(Ip,v) such that Γ \Ip,v is a compact orientable surface of genus g. Surp...
متن کاملUniform Lattices Acting on Some Hyperbolic Buildings
Let X be a 2-dimensional right-angled hyperbolic building. We characterise the set of covolumes of uniform lattices in Aut(X). We also show that the group Aut(X) admits an infinite ascending tower of uniform lattices.
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2006
ISSN: 1631-073X
DOI: 10.1016/j.crma.2005.11.020