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Group Actions on Manifolds
 
Edited by: Reinhard Schultz
Group Actions on Manifolds
eBook ISBN:  978-0-8218-7621-3
Product Code:  CONM/36.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Group Actions on Manifolds
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Group Actions on Manifolds
Edited by: Reinhard Schultz
eBook ISBN:  978-0-8218-7621-3
Product Code:  CONM/36.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 361985; 568 pp
    MSC: Primary 57; Secondary 55;

    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
     
     
    • Articles
    • Frank Raymond and Reinhard Schultz — The work and influence of Deane Montgomery [ MR 780952 ]
    • Reinhard Schultz — Bibliography of Deane Montgomery [ MR 780953 ]
    • Reinhard Schultz — Homotopy invariants and $G$-manifolds: a look at the past fifteen years [ MR 780954 ]
    • Ronald M. Dotzel — Splitting semifree finite group actions on homotopy spheres into solid tori [ MR 780955 ]
    • Sören Illman — Equivariant Whitehead torsion and actions of compact Lie groups [ MR 780956 ]
    • Christopher Allday — A family of unusual torus group actions [ MR 780957 ]
    • J.-P. Haeberly — For $G=S^1$ there is no $G$-Chern character [ MR 780958 ]
    • Peter Löffler and Reinhard Schultz — Equivariant frameability of homotopy linear $S^1$ actions on spheres [ MR 780959 ]
    • Benjamin M. Mann and Edward Y. Miller — Action maps on equivariant function spaces and applications to PL bordism [ MR 780960 ]
    • Alejandro Necochea — Borsuk-Ulam theorems for prime periodic transformation groups [ MR 780961 ]
    • Duane Randall — On equivariant maps of Stiefel manifolds [ MR 780962 ]
    • Sylvain E. Cappell and Julius L. Shaneson — Representations at fixed points [ MR 780963 ]
    • Karl Heinz Dovermann, Ted Petrie and Reinhard Schultz — Transformation groups and fixed point data [ MR 780964 ]
    • Mikiya Masuda and Ted Petrie — Lectures on transformation groups and Smith equivalence [ MR 780965 ]
    • Reinhard Schultz — Transformation groups and exotic spheres [ MR 780966 ]
    • Shmuel Weinberger — Constructions of group actions: a survey of some recent developments [ MR 780967 ]
    • Amir H. Assadi — Concordance of group actions on spheres [ MR 780968 ]
    • Eung Chun Cho and Dong Youp Suh — Induction in equivariant $K$-theory and $s$-Smith equivalence of representations [ MR 780969 ]
    • Eung Chun Cho — Smith equivalent representations of generalized quaternion groups [ MR 780970 ]
    • Dong Youp Suh — $s$-Smith equivalent representations of finite abelian groups [ MR 780971 ]
    • Yuh-Dong Tsai — Isotropy representations of nonabelian finite group actions [ MR 780972 ]
    • Allan L. Edmonds — Transformation groups and low-dimensional manifolds [ MR 780973 ]
    • Kyung Bai Lee and Frank Raymond — The role of Seifert fiber spaces in transformation groups [ MR 780974 ]
    • David Fried and Ronnie Lee — Realizing group automorphisms [ MR 780975 ]
    • Ronnie Lee and Steven H. Weintraub — Cohomology of a Siegel modular variety of degree $2$ [ MR 780976 ]
    • Hsü Tung Ku, Mei Chin Ku and L. N. Mann — Newman’s theorem and the Hilbert-Smith conjecture [ MR 780977 ]
    • H. Turner Laquer — Geometry, representation theory, and the Yang-Mills functional [ MR 780978 ]
    • Edited by R. Schultz — Problems submitted to the AMS summer research conference on group actions [ MR 780979 ]
  • 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: 361985; 568 pp
MSC: Primary 57; Secondary 55;

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.

  • Articles
  • Frank Raymond and Reinhard Schultz — The work and influence of Deane Montgomery [ MR 780952 ]
  • Reinhard Schultz — Bibliography of Deane Montgomery [ MR 780953 ]
  • Reinhard Schultz — Homotopy invariants and $G$-manifolds: a look at the past fifteen years [ MR 780954 ]
  • Ronald M. Dotzel — Splitting semifree finite group actions on homotopy spheres into solid tori [ MR 780955 ]
  • Sören Illman — Equivariant Whitehead torsion and actions of compact Lie groups [ MR 780956 ]
  • Christopher Allday — A family of unusual torus group actions [ MR 780957 ]
  • J.-P. Haeberly — For $G=S^1$ there is no $G$-Chern character [ MR 780958 ]
  • Peter Löffler and Reinhard Schultz — Equivariant frameability of homotopy linear $S^1$ actions on spheres [ MR 780959 ]
  • Benjamin M. Mann and Edward Y. Miller — Action maps on equivariant function spaces and applications to PL bordism [ MR 780960 ]
  • Alejandro Necochea — Borsuk-Ulam theorems for prime periodic transformation groups [ MR 780961 ]
  • Duane Randall — On equivariant maps of Stiefel manifolds [ MR 780962 ]
  • Sylvain E. Cappell and Julius L. Shaneson — Representations at fixed points [ MR 780963 ]
  • Karl Heinz Dovermann, Ted Petrie and Reinhard Schultz — Transformation groups and fixed point data [ MR 780964 ]
  • Mikiya Masuda and Ted Petrie — Lectures on transformation groups and Smith equivalence [ MR 780965 ]
  • Reinhard Schultz — Transformation groups and exotic spheres [ MR 780966 ]
  • Shmuel Weinberger — Constructions of group actions: a survey of some recent developments [ MR 780967 ]
  • Amir H. Assadi — Concordance of group actions on spheres [ MR 780968 ]
  • Eung Chun Cho and Dong Youp Suh — Induction in equivariant $K$-theory and $s$-Smith equivalence of representations [ MR 780969 ]
  • Eung Chun Cho — Smith equivalent representations of generalized quaternion groups [ MR 780970 ]
  • Dong Youp Suh — $s$-Smith equivalent representations of finite abelian groups [ MR 780971 ]
  • Yuh-Dong Tsai — Isotropy representations of nonabelian finite group actions [ MR 780972 ]
  • Allan L. Edmonds — Transformation groups and low-dimensional manifolds [ MR 780973 ]
  • Kyung Bai Lee and Frank Raymond — The role of Seifert fiber spaces in transformation groups [ MR 780974 ]
  • David Fried and Ronnie Lee — Realizing group automorphisms [ MR 780975 ]
  • Ronnie Lee and Steven H. Weintraub — Cohomology of a Siegel modular variety of degree $2$ [ MR 780976 ]
  • Hsü Tung Ku, Mei Chin Ku and L. N. Mann — Newman’s theorem and the Hilbert-Smith conjecture [ MR 780977 ]
  • H. Turner Laquer — Geometry, representation theory, and the Yang-Mills functional [ MR 780978 ]
  • Edited by R. Schultz — Problems submitted to the AMS summer research conference on group actions [ MR 780979 ]
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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