Rigidity in Dynamics and Geometry : Contributions From the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences Cambridge, United Kingdom, 5 January – 7 July 2000

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan­ uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else. Front Matter....Pages I-XIII Quasi-Conformal Geometry and Hyperbolic Geometry....Pages 1-17 On and Around the Bounded Cohomology of SL 2 ....Pages 19-37 Densité d’orbites d’actions de groupes linéaires et propriétés d’équidistribution de marches aléatoires....Pages 39-76 Exceptional Sets in Dynamical Systems and Diophantine Approximation....Pages 77-98 An Introduction to Cocycle Super-Rigidity....Pages 99-134 Rigid Geometric Structures and Representations of Fundamental Groups....Pages 135-147 Coarse-Geometric Perspective on Negatively Curved Manifolds and Groups....Pages 149-166 On Orbit Equivalence of Measure Preserving Actions....Pages 167-186 The Margulis Invariant of Isometric Actions on Minkowski (2+1)-Space....Pages 187-201 Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group....Pages 203-226 Appendix: Diophantine Approximation on Hyperbolic Surfaces....Pages 227-236 Bounded Cohomology, Boundary Maps, and Rigidity of Representations into Homeo + (S 1 ) and SU(1, n )....Pages 237-260 SAT Actions and Ergodic Properties of the Horosphere Foliation....Pages 261-282 Nonexpanding Maps, Busemann Functions, and Multiplicative Ergodic Theory....Pages 283-294 The Phase Space of k- Surfaces....Pages 295-307 Schottky Subgroups of Mapping Class Groups and the Geometry of Surface-by-Free Groups....Pages 309-319 Actions of Semisimple Lie Groups with Stationary Measure....Pages 321-343 On the Cohomology of Anosov Actions....Pages 345-361 Harmonic Analysis and Hecke Operators....Pages 363-378 L p -Cohomology and Pinching....Pages 379-389 Classical and Non-Linearity Properties of Kac-Moody Lattices....Pages 391-406 Actions of Maximal Tori on Homogeneous Spaces....Pages 407-424 Dynamics on Parameter Spaces: Submanifold and Fractal Subset Questions....Pages 425-440 Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups....Pages 441-457 Square Tiled Surfaces and Teichmüller Volumes of the Moduli Spaces of Abelian Differentials....Pages 459-471 On Property (T) for Discrete Groups....Pages 473-482 Back Matter....Pages 483-492 From the contents: M. Bourdon, H. Pajot: Quasi-Conformal Geometry and Hyperbolic Geometry M. Burger, N. Monod: On and Around the Bounded Cohomology of SL2 J.-P. Conze, Y. Guivarc'h: Densité d'orbites d'actions de groupes linéaires et propriétés d'équidistribution de marches aléatoires M. Dodson: Exceptional Sets in Dynamical Systems and Diophantine Approximation R. Feres: An Introduction to Cocycle Super-Rigidity D. Fisher: Rigid Geometric Structures and Representations of Fundamental Groups A. Furman: Coarse-Geometric Perspective on Negatively Curved Manifolds and Groups D. Gaboriau: On Orbit Equivalence of Measure Preserving Actions W.M. Goldman: The Margulis Invariant of Isometric Actions on Minkowski (2+1)-Space S. Hersonsky, F. Paulin: Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group A. Iozzi: Bounded Cohomology, Boundary Maps, and Rigidity of Representations. This volume is an offspring of the special semester "Ergodic Theory, Geometric Rigidity and Number Theory" held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from January until July, 2000. Some of the major recent developments in rigidity theory, geometric group theory, flows on homogeneous spaces and Teichmüller spaces, quasi-conformal geometry, negatively curved groups and spaces, Diophantine approximation, and bounded cohomology are presented here. The authors have given special consideration to making the papers accessible to graduate students, with most of the contributions starting at an introductory level and building up to presenting topics at the forefront in this active field of research. The volume contains surveys and original unpublished results as well, and is an invaluable source also for the experienced researcher.