Journal ArticleDOI
Rigidity of spherical buildings and joins
Reads0
Chats0
TLDR
In this article, the authors prove a rigidity and a characterization result for building and spherical joins using sets of antipodal points, and prove that these points can be used for building construction.Abstract:
We prove a rigidity and a characterization result for buildings and spherical joins using sets of antipodal points.read more
Citations
More filters
Journal ArticleDOI
Isometry groups of non-positively curved spaces: structure theory
TL;DR: In this paper, the structure theory of full isometry groups of locally compact non-positively curved metric spaces is developed, including de Rham decompositions, normal subgroup structure, and characterizing properties of symmetric spaces and Bruhat-Tits buildings.
Journal ArticleDOI
At infinity of finite-dimensional CAT(0) spaces
TL;DR: In this article, it was shown that any filtering family of closed convex subsets of a finite-dimensional CAT(0) space X has a non-empty intersection in the visual bordification (X) over bar = X boolean OR partial derivative X.
Journal ArticleDOI
Isometry groups of non-positively curved spaces: structure theory
TL;DR: In this paper, the structure theory of full isometry groups of locally compact non-positively curved metric spaces is developed, including de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat-Tits buildings.
Journal ArticleDOI
Braids, posets and orthoschemes
Thomas Brady,Jon McCammond +1 more
TL;DR: In this article, the curvature properties of the order complex of a bounded graded poset under a metric called the orthoscheme metric were studied and it was shown that the 5-string braid group is the fundamental group of a compact nonpositively curved space.
References
More filters
Book
Metric Spaces of Non-Positive Curvature
TL;DR: In this article, the authors describe the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries.
Journal ArticleDOI
Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
Bruce Kleiner,Bernhard Leeb +1 more
TL;DR: In this paper, the authors studied quasi-isometries between products of symmetric spaces and Euclidean buildings, and showed that the latter preserve the product structure and the latter are at finite distance from homotheties.
Journal ArticleDOI
The local structure of length spaces with curvature bounded above
TL;DR: In this article, it was shown that if X is a locally compact CAT(0) space with cocompact isometry group, then the dimension of the Tits boundary and the asymptotic cone(s) of X are determined by the maximal dimension of a flat in X.
Journal ArticleDOI
Manifolds of nonpositive curvature and their buildings
TL;DR: In this paper, a topological Tits building is constructed for a complete Riemannian manifold of bounded nonpositive sectional curvature and finite volume, and it is shown that it is a building associated with a Lie group.