Contemporary Mathematics 1988; 312 pp; softcover Volume: 74 ISBN10: 0821850822 ISBN13: 9780821850824 List Price: US$49 Member Price: US$39.20 Order Code: CONM/74
 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 AMSIMSSIAM 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  W. Abikoff  Kleinian groupsgeometrically finite and geometrically perverse
 G. W. Brumfiel  The real spectrum compactification of Teichmuller space
 G. W. Brumfiel  A semialgebraic Brower fixed point theorem for real affine space
 G. W. Brumfiel  The tree of a nonarchimedean hyperbolic plane
 K. Corlette  Gauge theory and representations of Kahler groups
 D. R. Farkas  The Diophantine nature of some constructions at infinity
 B. Fine and G. Rosenberger  Complex representations and onerelator products of cyclics
 M. Gerstenhaber and S. D. Schack  Sometimes \(H^1\) is \(H^2\) and discrete groups deform
 W. M. Goldman  Geometric structures on manifolds and varieties of representations
 W. M. Goldman and Y. Kamishima  Topological rigidity of developing maps with applications to conformally flat structures
 W. J. Harvey  Modular groups and representation spaces
 A. Lubotzky and A. R. Magid  Local structures of representation varieties: examples
 J. J. Millson  Deformations of representations of finitely generated groups
 K. Morrison  Connected components of representation varieties
 J. O'Halloran  A characterization of orbit closure
 R. C. Penner  Calculus on moduli spaces
 D. M. Snow  Affine homogeneous spaces
 C. W. Stark  Deformations and discrete subgroups of loop groups
