Geometry, Topology, and Dynamics in Negative Curvature

C. S. Aravinda, F. T. Farrell, J. -F. Lafont

• Publisher: Cambridge University Press
• Year: 2016
• Print ISBN: 9781107529007
• eBook ISBN: 9781316540909
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.

Table of contents

• Cover
• Series page
• Title
• Copyright
• Contents
• List of contributors
• Preface
• 1 Gap distributions and homogeneous dynamics
• 2 Topology of open nonpositively curved manifolds
• 3 Cohomologie et actions isométriques propres sur les espaces L(sub[p])
• 4 Compact Clifford–Klein Forms – Geometry, Topology and Dynamics
• 5 A survey on noncompact harmonic and asymptotically harmonic manifolds
• 6 The Atiyah conjecture
• 7 Cannon-Thurston Maps for Surface Groups: An Exposition of Amalgamation Geometry and Split Geometry
• 8 Counting visible circles on the sphere and Kleinian groups
• 9 Counting arcs in negative curvature
• 10 Lattices in hyperbolic buildings