Description
Book SynopsisThis volume is based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010.Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is otherwise available only in specialized texts. Topics include hyperbolic structures on surfaces and their degenerations, applications of ping-pong lemmas in various contexts, introductions to Lorenzian and complex hyperbolic geometry, and representation varieties of surface groups into PSL(2, ℝ) and other semi-simple Lie groups. This volume will serve as a useful portal to students and researchers in a vibrant and multi-faceted area of mathematics.
Table of ContentsAn Invitation to Elementary Hyperbolic Geometry (Ying Zhang); Hyperbolic Structures on Surfaces (Javier Aramayona); Degenerations of Hyperbolic Structures on Surfaces (Chris Leininger); Ping-Pong Lemmas with Applications to Geometry and Topology (Thomas Michael Koberda); Creating Software for Visualizing Kleinian Groups (Yasushi Yamashita); Traces in Complex Hyperbolic Geometry (John Parker); Lorentzian Geometry (Todd Drumm); Connected Components of Representation Spaces (Frederic Palesi); Rigidity And Flexibility of Surface Groups in Semisimple Lie Groups (Inkang Kim); Abelian and Non-Abelian Cohomology (Eugene Xia).
