Geometry, Topology, and Dynamics in Negative Curvature

Klappentext 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. Zusammenfassung Negative curvature arises in several mathematical areas, including geometry, topology, dynamics, and number theory. This volume contains survey articles around this common theme, which should help mathematicians interested in transitioning between these areas, as well as graduate students entering this interdisciplinary subject. Inhaltsverzeichnis Preface C. S. Aravinda, F. T. Farrell and J.-F. Lafont; 1. Gap distributions and homogeneous dynamics Jayadev S. Athreya; 2. Topology of open nonpositively curved manifolds Igor Belegradek; 3. Cohomologie et actions isométriques propres sur les espaces Lp Marc Bourdon; 4. Compact Clifford-Klein forms - geometry, topology and dynamics David Constantine; 5. A survey on noncompact harmonic and asymptotically harmonic manifolds Gerhard Knieper; 6. The Atiyah conjecture Peter A. Linnell; 7. Cannon-Thurston maps for surface groups - an exposition of amalgamation geometry and split geometry Mahan Mj; 8. Counting visible circles on the sphere and Kleinian groups Hee Oh and Nimish Shah; 9. Counting arcs in negative curvature Jouni Parkkonen and Frédéric Paulin; 10. Lattices in hyperbolic buildings Anne Thomas. ...

Zusammenfassung
Negative curvature arises in several mathematical areas, including geometry, topology, dynamics, and number theory. This volume contains survey articles around this common theme, which should help mathematicians interested in transitioning between these areas, as well as graduate students entering this interdisciplinary subject.

Inhalt

Preface C. S. Aravinda, F. T. Farrell and J.-F. Lafont; 1. Gap distributions and homogeneous dynamics Jayadev S. Athreya; 2. Topology of open nonpositively curved manifolds Igor Belegradek; 3. Cohomologie et actions isométriques propres sur les espaces Lp Marc Bourdon; 4. Compact Clifford-Klein forms - geometry, topology and dynamics David Constantine; 5. A survey on noncompact harmonic and asymptotically harmonic manifolds Gerhard Knieper; 6. The Atiyah conjecture Peter A. Linnell; 7. Cannon-Thurston maps for surface groups - an exposition of amalgamation geometry and split geometry Mahan Mj; 8. Counting visible circles on the sphere and Kleinian groups Hee Oh and Nimish Shah; 9. Counting arcs in negative curvature Jouni Parkkonen and Frédéric Paulin; 10. Lattices in hyperbolic buildings Anne Thomas.