**Contemporary Mathematics**

Volume: 74;
1988;
312 pp;
Softcover

MSC: Primary 20;
Secondary 32; 57

Print ISBN: 978-0-8218-5082-4

Product Code: CONM/74

List Price: $49.00

Individual Member Price: $39.20

**Electronic ISBN: 978-0-8218-7663-3
Product Code: CONM/74.E**

List Price: $49.00

Individual Member Price: $39.20

# Geometry of Group Representations

Share this page *Edited by *
*William M. Goldman; Andy R. Magid*

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

# Table of Contents

## Geometry of Group Representations

- Table of Contents ix10 free
- Preface xi12 free
- List of Participants xiii14 free
- List of Talks xv16 free
- Kleinian Groups – Geometrically Finite and Geometrically Perverse 118 free
- The Real Spectrum Compactification of Teichmuller Space 5168
- A Semi-Algebraic Brower Fixed Point Theorem for Real Affine Space 7794
- The Tree of a Non-Archimedean Hyperbolic Plane 83100
- Gauge Theory and Representations of Kahler Groups 107124
- The Diophantine Nature of Some Constructions at Infinity 125142
- Complex Representations and One-Relator Products of Cyclics 131148
- Sometimes H1 is H2 and Discrete Groups Deform 149166
- Geometric Structures on Manifolds and Varieties of Representations 169186
- Topological Rigidity of Developing Maps with Applications to Conformally Flat Structures 199216
- Modular Groups and Representation Spaces 205222
- Local Structures of Representation Varieties: Examples 215232
- Deformations of Representations of Finitely Generated Groups 237254
- Connected Components of Representation Varieties 255272
- A Characterization of Orbit Closure 271288
- Calculus on Moduli Spaces 277294
- Affine Homogeneous Spaces 295312
- Deformations and Discrete Subgroups of Loop Groups 301318
- Afterword 311328