Contemporary Mathematics 1985; 568 pp; softcover Volume: 36 Reprint/Revision History: reprinted 1989 ISBN10: 0821850385 ISBN13: 9780821850381 List Price: US$70 Member Price: US$56 Order Code: CONM/36
 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 AMSIMSSIAM 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
HomotopyTheoretic 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  BorsukUlam 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
Lowdimensional Topology and Transformation Groups  A. Edmonds  Transformation groups and lowdimensional 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 HilbertSmith conjecture
 H. T. Laquer  Geometry, representation theory, and the YangMills functional
Problems  R. Schultz  Problems submitted to the AMS Summer Research Conference on Group Actions
