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Geometry of Group Representations
Edited by: William M. Goldman and Andy R. Magid
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Contemporary Mathematics
1988; 312 pp; softcover
Volume: 74
ISBN-10: 0-8218-5082-2
ISBN-13: 978-0-8218-5082-4
List Price: US$46
Member Price: US$36.80
Order Code: CONM/74
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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

  • W. Abikoff -- Kleinian groups--geometrically finite and geometrically perverse
  • G. W. Brumfiel -- The real spectrum compactification of Teichmuller space
  • G. W. Brumfiel -- A semi-algebraic Brower fixed point theorem for real affine space
  • G. W. Brumfiel -- The tree of a non-archimedean 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 one-relator 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
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