منابع مشابه
Infinite generation of non-cocompact lattices on right-angled buildings
Tree lattices have been well-studied (see [BL]). Less understood are lattices on higherdimensional CAT(0) complexes. In this paper, we consider lattices on X a locally finite, regular right-angled building (see Davis [D] and Section 1 below). Examples of such X include products of locally finite regular or biregular trees, or Bourdon’s building Ip,q [B], which has apartments hyperbolic planes t...
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.
متن کاملLattices acting on right-angled buildings
Let X be a right-angled building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of groups to compl...
متن کاملLattices Acting on Right-angled Hyperbolic Buildings
Let X be a right-angled hyperbolic building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of grou...
متن کاملLattices in Hyperbolic Buildings
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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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2014
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089514000287