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Geometry of Group Representations
 
Geometry of Group Representations
eBook ISBN:  978-0-8218-7663-3
Product Code:  CONM/74.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Geometry of Group Representations
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Geometry of Group Representations
eBook ISBN:  978-0-8218-7663-3
Product Code:  CONM/74.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 741988; 312 pp
    MSC: Primary 20; Secondary 32; 57;

    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
     
     
    • Articles
    • William Abikoff — Kleinian groups—geometrically finite and geometrically perverse [ MR 957510 ]
    • G. W. Brumfiel — The real spectrum compactification of Teichmüller space [ MR 957511 ]
    • G. W. Brumfiel — A semi-algebraic Brouwer fixed point theorem for real affine space [ MR 957512 ]
    • G. W. Brumfiel — The tree of a non-Archimedean hyperbolic plane [ MR 957513 ]
    • Kevin Corlette — Gauge theory and representations of Kähler groups [ MR 957514 ]
    • Daniel R. Farkas — The Diophantine nature of some constructions at infinity [ MR 957515 ]
    • Benjamin Fine and Gerhard Rosenberger — Complex representations and one-relator products of cyclics [ MR 957516 ]
    • Murray Gerstenhaber and Samuel D. Schack — Sometimes $H^1$ is $H^2$ and discrete groups deform [ MR 957517 ]
    • William M. Goldman — Geometric structures on manifolds and varieties of representations [ MR 957518 ]
    • William M. Goldman and Yoshinobu Kamishima — Topological rigidity of developing maps with applications to conformally flat structures [ MR 957519 ]
    • W. J. Harvey — Modular groups and representation spaces [ MR 957520 ]
    • Alexander Lubotzky and Andy R. Magid — Local structure of representation varieties: examples [ MR 957521 ]
    • John J. Millson — Deformations of representations of finitely generated groups [ MR 957522 ]
    • Kent Morrison — Connected components of representation varieties [ MR 957523 ]
    • Joyce O’Halloran — A characterization of orbit closure [ MR 957524 ]
    • R. C. Penner — Calculus on moduli space [ MR 957525 ]
    • Dennis M. Snow — Affine homogeneous spaces [ MR 957526 ]
    • Christopher W. Stark — Deformations and discrete subgroups of loop groups [ MR 957527 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 741988; 312 pp
MSC: Primary 20; Secondary 32; 57;

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.

  • Articles
  • William Abikoff — Kleinian groups—geometrically finite and geometrically perverse [ MR 957510 ]
  • G. W. Brumfiel — The real spectrum compactification of Teichmüller space [ MR 957511 ]
  • G. W. Brumfiel — A semi-algebraic Brouwer fixed point theorem for real affine space [ MR 957512 ]
  • G. W. Brumfiel — The tree of a non-Archimedean hyperbolic plane [ MR 957513 ]
  • Kevin Corlette — Gauge theory and representations of Kähler groups [ MR 957514 ]
  • Daniel R. Farkas — The Diophantine nature of some constructions at infinity [ MR 957515 ]
  • Benjamin Fine and Gerhard Rosenberger — Complex representations and one-relator products of cyclics [ MR 957516 ]
  • Murray Gerstenhaber and Samuel D. Schack — Sometimes $H^1$ is $H^2$ and discrete groups deform [ MR 957517 ]
  • William M. Goldman — Geometric structures on manifolds and varieties of representations [ MR 957518 ]
  • William M. Goldman and Yoshinobu Kamishima — Topological rigidity of developing maps with applications to conformally flat structures [ MR 957519 ]
  • W. J. Harvey — Modular groups and representation spaces [ MR 957520 ]
  • Alexander Lubotzky and Andy R. Magid — Local structure of representation varieties: examples [ MR 957521 ]
  • John J. Millson — Deformations of representations of finitely generated groups [ MR 957522 ]
  • Kent Morrison — Connected components of representation varieties [ MR 957523 ]
  • Joyce O’Halloran — A characterization of orbit closure [ MR 957524 ]
  • R. C. Penner — Calculus on moduli space [ MR 957525 ]
  • Dennis M. Snow — Affine homogeneous spaces [ MR 957526 ]
  • Christopher W. Stark — Deformations and discrete subgroups of loop groups [ MR 957527 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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