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Group Actions on Manifolds
Edited by: Reinhard Schultz
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Contemporary Mathematics
1985; 568 pp; softcover
Volume: 36
Reprint/Revision History:
reprinted 1989
ISBN-10: 0-8218-5038-5
ISBN-13: 978-0-8218-5038-1
List Price: US$70
Member Price: US$56
Order Code: CONM/36
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Not merely an account of new results, this book is also a guide to motivation behind present work and potential future developments. Readers can obtain an overall understanding of the sorts of problems one studies in group actions and the methods used to study such problems. The book will be accessible to advanced graduate students who have had the equivalent of three semesters of graduate courses in topology; some previous acquaintance with the fundamentals of transformation groups is also highly desirable.

The articles in this book are mainly based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado. A major objective was to provide an overall account of current knowledge in transformation groups; a number of survey articles describe the present state of the subject from several complementary perspectives. The book also contains some research articles, generally dealing with results presented at the conference. Finally, there is a discussion of current problems on group actions and an acknowledgment of the work and influence of D. Montgomery on the subject.

Table of Contents

  • F. Raymond and R. Schultz -- The work and influence of Deane Montgomery
  • Bibliography of Deane Montgomery
Homotopy-Theoretic Techniques and Applications
  • R. Schultz -- Homotopy invariants and \(G\)-manifolds: A look at the past fifteen years
  • R. Dotzel -- Splitting semifree group actions on homotopy spheres into solid tori
  • S. Illman -- Equivariant Whitehead torsion and actions of compact Lie groups
Homological Methods and Machinery
  • C. Allday -- A family of unusual torus group actions
  • J.-P. Haeberly -- For \(G=S^1\) there is no \(G\)-Chern character
  • P. Löffler and R. Schultz -- Equivariant frameability of homotopy linear \(S^1\) actions on spheres
  • B. M. Mann and E. Y. Miller -- Action maps on equivariant function spaces and applications to \(PL\) bordism
  • A. Necochea -- Borsuk-Ulam theorems for prime periodic transformation groups
  • D. Randall -- On equivariant maps of Stiefel manifolds
Applications of Surgery and Geometric Topology
  • S. Cappell and J. Shaneson -- Representations at fixed points
  • K. H. Dovermann, T. Petrie, and R. Schultz -- Transformation groups and fixed point data
  • M. Masuda and T. Petrie -- Lectures on transformation groups and Smith equivalence
  • R. Schultz -- Transformation groups and exotic spheres
  • S. Weinberger -- Constructions of group actions:A survey of recent developments
  • A. Assadi -- Concordance of group actions on spheres
  • E. C. Cho and D. Y. Suh -- Induction in equivariant \(K\)-theory and \(s\)-Smith equivalence of representations
  • E. C. Cho -- Smith equivalent representations of generalized quaternion groups
  • D. Y. Suh -- \(s\)-Smith equivalent representations for finite abelian groups
  • Y. D. Tsai -- Isotropy representations of nonabelian finite group actions
Low-dimensional Topology and Transformation Groups
  • A. Edmonds -- Transformation groups and low-dimensional manifolds
Homogeneous Spaces and Seifert Fiberings
  • K. B. Lee and F. Raymond -- The role of Seifert fiber spaces in transformation groups
  • D. Fried and R. Lee -- Realizing group automorphisms
  • R. Lee and S. Weintraub -- Cohomology of a Siegel modular variety of degree two
Transformation Groups and Differential Geometry
  • H. T. Ku, M. C. Ku, and L. N. Mann -- Newman's theorem and the Hilbert-Smith conjecture
  • H. T. Laquer -- Geometry, representation theory, and the Yang-Mills functional
Problems
  • R. Schultz -- Problems submitted to the AMS Summer Research Conference on Group Actions
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