Title | Proceedings of the Conference on Transformation Groups [electronic resource] : New Orleans, 1967 / edited by Paul S. Mostert |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1968 |

Connect to | http://dx.doi.org/10.1007/978-3-642-46141-5 |

Descript | XIV, 458 p. online resource |

SUMMARY

These Proceedings contain articles based on the lectures and inยญ formal discussions at the Conference on Transformation Groups held at Tulane University, May 8 to June 2, 1967 under the sponsorship of the Advanced Science Seminar Projects of the National Science Founยญ dation (Contract No. GZ 400). They differ, however, from many such Conference proceedings in that particular emphasis has been given to the review and exposition of the state of the theory in its various maniยญ festations, and the suggestion of direction to further research, rather than purely on the publication of research papers. That is not to say that there is no new material contained herein. On the contrary, there is an abundance of new material, many new ideas, new questions, and new conjecturesãrefully incorporated within the framework of the theory as the various authors see it. An original objective of the Conference and of this report was to supply a much needed review of and supplement to the theory since the publication of the three standard works, MONTGOMERY and ZIPPIN, Topological Transformation Groups, Interscience Pubยญ lishers, 1955, BOREL et aI. , Seminar on Transformation Groups, Annals of Math. Surveys, 1960, and CONNER and FLOYD, Differenยญ tial Periodic Maps, Springer-Verlag, 1964. Considering this objective ambitious enough, it was decided to limit the survey to that part of Transformation Group Theory derived from the Montgomery School

CONTENT

Surgery and the Theory of Differentiable Transformation Groups -- I Differentiable Transformation Groups -- Exotic Actions on Spheres -- A Survey on Regularity Theorems in Differentiable Compact Transformation Groups -- Differentiable Actions on Homotopy Seven Spheres, II -- On the Classification of Regular O(n)-Manifolds in Terms of their Orbit Bundles -- Involutions on Homotopy Spheres -- Involutionen auf Mannigfaltigkeiten -- Some Results on Involutions of Homotopy Spheres -- Free Differentiable Actions on Homotopy Spheres -- Some Results on Cyclic Transformation Groups on Homotopy Spheres -- Examples of Free Involutions on 3-Manifolds -- Short Notes -- Cyclic Group Actions on Homotopy Spheres -- Non-Existence of Free Differentiable Actions of S1 and ?2 on Homotopy Spheres -- On Differentiable Actions of Compact Lie Groups on Compact Manifolds -- Examples of Differentiable Involutions -- 3-Dimensional G-Manifolds with 2-Dimensional Orbits -- Some Problems in Differentiable Transformation Groups -- Problems -- II Algebraic Topological and Other Techniques -- Equivariant Homology Theories -- Cohomological Aspects of Transformation Groups -- Equivariant Homotopy -- Gaps in the Dimensions of Compact Transformation Groups -- Actions of SO (2) on 3-Manifolds -- The Fixed Point Set of Zp in a C* (m1, m2,..., mq-1; Zp)-Space -- Group Actions and a Spectral Sequence -- Short Notes -- Exotic PL Actions which are Topologically Linear -- The Lefschetz Fixed Point Theorem for Involutions -- Involutions on the n-Cell -- Topological Actions do not Necessarily have Reasonable Slices -- A Simple Proof of the Maximal Tori Theorem of E. Cartan -- A Relation between Group Actions and Index -- An Example -- Problems -- III Compact (Non-Lie) Transformation Groups -- Cohomological and Dimension Theoretical Properties of Orbit Spaces of p-Adic Actions -- Compact Non-Lie Groups -- Applications of Transformation Groups to Problems in Topological Semigroups -- On the Action of Compact Groups -- A Generalization of the Conner Inequalities -- Short Notes -- Some Simple Observations about Ap-Actions -- Problems -- IV Non-Compact Transformation Groups -- On Hilbertโ{128}{153}s Theory of Closed Group Actions -- On the Variation of Isotropy Subalgebras -- Non-Compact Lie Group Actions -- Fixed Point Sets of Transformation Groups on Separable Infinite-Dimensional Frechet Spaces -- On a Kind of Discrete Transformation Group -- Problems

Mathematics
Algebra
Mathematics
Algebra