scholarly journals Large scale geometry of negatively curved ℝn⋊ ℝ

2014 ◽  
Vol 18 (2) ◽  
pp. 831-872 ◽  
Author(s):  
Xiangdong Xie
Keyword(s):  
Large Scale ◽  
Negatively Curved ◽  
Large Scale Geometry

On Finsler manifolds of negative flag curvature

2015 ◽  
Vol 07 (03) ◽  
pp. 483-504 ◽  
Author(s):  
Yong Fang ◽  
Patrick Foulon
Keyword(s):  
Geodesic Flow ◽  
Large Scale ◽  
Riemannian Metrics ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Metric Entropy ◽  
Hadamard Manifolds ◽  
Finsler Manifolds ◽  
Negatively Curved ◽  
Large Scale Geometry

One of the key differences between Finsler metrics and Riemannian metrics is the non-reversibility, i.e. given two points p and q, the Finsler distance d(p, q) is not necessarily equal to d(q, p). In this paper, we build the main tools to investigate the non-reversibility in the context of large-scale geometry of uniform Finsler Cartan–Hadamard manifolds. In the second part of this paper, we use the large-scale geometry to prove the following dynamical theorem: Let φ be the geodesic flow of a closed negatively curved Finsler manifold. If its Anosov splitting is C2, then its cohomological pressure is equal to its Liouville metric entropy. This result generalizes a previous Riemannian result of U. Hamenstädt.

Large-Scale Geometry of Montana Thrust Belt: ABSTRACT

AAPG Bulletin ◽  
1986 ◽  
Vol 70 ◽  
Author(s):  
James W. Sears, David M. Dolberg
Keyword(s):  
Large Scale ◽  
Thrust Belt ◽  
Large Scale Geometry

scholarly journals The large-scale geometry of Hilbert modular groups

1996 ◽  
Vol 44 (3) ◽  
pp. 435-478 ◽  
Author(s):  
Benson Farb ◽  
Richard Schwartz
Keyword(s):  
Large Scale ◽  
Large Scale Geometry ◽  
Modular Groups ◽  
Hilbert Modular

scholarly journals Book Review: Large scale geometry

2014 ◽  
Vol 52 (1) ◽  
pp. 141-149
Author(s):  
Shmuel Weinberger
Keyword(s):  
Large Scale ◽  
Large Scale Geometry

scholarly journals Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups

2021 ◽  
pp. 1-27
Author(s):  
S. Arora ◽  
I. Castellano ◽  
G. Corob Cook ◽  
E. Martínez-Pedroza
Keyword(s):  
Large Scale ◽  
Cohomological Dimension ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Discrete Groups ◽  
Locally Compact ◽  
Amalgamated Free Products ◽  
Negatively Curved ◽  
Dimension Formula ◽  
Totally Disconnected

This paper is part of the program of studying large-scale geometric properties of totally disconnected locally compact groups, TDLC-groups, by analogy with the theory for discrete groups. We provide a characterization of hyperbolic TDLC-groups, in terms of homological isoperimetric inequalities. This characterization is used to prove the main result of this paper: for hyperbolic TDLC-groups with rational discrete cohomological dimension [Formula: see text], hyperbolicity is inherited by compactly presented closed subgroups. As a consequence, every compactly presented closed subgroup of the automorphism group [Formula: see text] of a negatively curved locally finite [Formula: see text]-dimensional building [Formula: see text] is a hyperbolic TDLC-group, whenever [Formula: see text] acts with finitely many orbits on [Formula: see text]. Examples where this result applies include hyperbolic Bourdon’s buildings. We revisit the construction of small cancellation quotients of amalgamated free products, and verify that it provides examples of hyperbolic TDLC-groups of rational discrete cohomological dimension [Formula: see text] when applied to amalgamated products of profinite groups over open subgroups. We raise the question of whether our main result can be extended to locally compact hyperbolic groups if rational discrete cohomological dimension is replaced by asymptotic dimension. We prove that this is the case for discrete groups and sketch an argument for TDLC-groups.

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