Geometry of Group Representations

The representations of a finitely generated group in a topological group $G$ form a topological space which is an analytic variety if $G$ is a Lie group, or an algebraic variety if $G$ is an algebraic group. The study of this area draws from and contributes to a wide range of mathematical subjects: algebra, analysis, topology, differential geometry, representation theory, and even mathematical physics. In some cases, the space of representations is the object of the study, in others it is a tool in a program of investigation, and, in many cases, it is both. Most of the papers in this volume are based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987.The conference was designed to bring together researchers from the diverse areas of mathematics involving spaces of group representations. In keeping with the spirit of the conference, the papers are directed at nonspecialists, but contain technical developments to bring the subject to the current research frontier. Some of the papers include entirely new results. Readers will gain an understanding of the present state of research in the geometry of group representations and their applications.

Table of Contents:
Kleinian groups---geometrically finite and geometrically perverse by W. Abikoff The real spectrum compactification of Teichmuller space by G. W. Brumfiel A semi-algebraic Brower fixed point theorem for real affine space by G. W. Brumfiel The tree of a non-archimedean hyperbolic plane by G. W. Brumfiel Gauge theory and representations of Kahler groups by K. Corlette The Diophantine nature of some constructions at infinity by D. R. Farkas Complex representations and one-relator products of cyclics by B. Fine and G. Rosenberger Sometimes $H^1$ is $H^2$ and discrete groups deform by M. Gerstenhaber and S. D. Schack Geometric structures on manifolds and varieties of representations by W. M. Goldman Topological rigidity of developing maps with applications to conformally flat structures by W. M. Goldman and Y. Kamishima Modular groups and representation spaces by W. J. Harvey Local structures of representation varieties: examples by A. Lubotzky and A. R. Magid Deformations of representations of finitely generated groups by J. J. Millson Connected components of representation varieties by K. Morrison A characterization of orbit closure by J. O'Halloran Calculus on moduli spaces by R. C. Penner Affine homogeneous spaces by D. M. Snow Deformations and discrete subgroups of loop groups by C. W. Stark.