Proceedings of the Conference on Transformation Groups: New Orleans, 1967

Description

These Proceedings contain articles based on the lectures and in­ 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 Foun­ 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 mani­ 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 conjectures~arefully 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 Pub­ lishers, 1955, BOREL et aI. , Seminar on Transformation Groups, Annals of Math. Surveys, 1960, and CONNER and FLOYD, Differen­ 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. Front Matter....Pages I-XIII Surgery and the Theory of Differentiable Transformation Groups....Pages 1-46 Exotic Actions on Spheres....Pages 47-76 A Survey on Regularity Theorems in Differentiable Compact Transformation Groups....Pages 77-124 Differentiable Actions on Homotopy Seven Spheres, II....Pages 125-134 On the Classification of Regular O ( n )-Manifolds in Terms of their Orbit Bundles....Pages 135-142 Involutions on Homotopy Spheres....Pages 143-147 Involutionen auf Mannigfaltigkeiten....Pages 148-166 Some Results on Involutions of Homotopy Spheres....Pages 167-174 Free Differentiable Actions on Homotopy Spheres....Pages 175-192 Some Results on Cyclic Transformation Groups on Homotopy Spheres....Pages 193-204 Examples of Free Involutions on 3-Manifolds....Pages 205-206 Cyclic Group Actions on Homotopy Spheres....Pages 207-207 Non-Existence of Free Differentiable Actions of S 1 and ℤ 2 on Homotopy Spheres....Pages 208-209 On Differentiable Actions of Compact Lie Groups on Compact Manifolds....Pages 210-213 Examples of Differentiable Involutions....Pages 214-219 3-Dimensional G-Manifolds with 2-Dimensional Orbits....Pages 220-222 Some Problems in Differentiable Transformation Groups....Pages 223-234 Back Matter....Pages 235-236 Equivariant Homology Theories....Pages 237-244 Cohomological Aspects of Transformation Groups....Pages 245-280 Equivariant Homotopy....Pages 281-292 Gaps in the Dimensions of Compact Transformation Groups....Pages 293-296 Actions of SO (2) on 3-Manifolds....Pages 297-318 The Fixed Point Set of Z p in a C * ( m 1 , m 2 , ..., m q -1 ; Z p )-Space....Pages 319-324 Group Actions and a Spectral Sequence....Pages 325-338 Exotic PL Actions which are Topologically Linear....Pages 339-340 The Lefschetz Fixed Point Theorem for Involutions....Pages 341-342 Involutions of the n -Cell....Pages 343-344 Topological Actions do not Necessarily have Reasonable Slices....Pages 345-345 A Simple Proof of the Maximal Tori Theorem of E. Cartan....Pages 346-348 A Relation between Group Actions and Index....Pages 349-350 An Example....Pages 351-351 Cohomological and Dimension Theoretical Properties of Orbit Spaces of p -Adic Actions....Pages 354-365 Compact Non-Lie Groups....Pages 366-369 Applications of Transformation Groups to Problems in Topological Semigroups....Pages 370-380 On the Action of Compact Groups....Pages 381-400 A Generalization of the Conner Inequalities....Pages 401-414 Some Simple Observations about A p Actions....Pages 415-417 On Hilberths Theory of Closed Group Actions....Pages 419-428 On the Variation of Isotropy Subalgebras....Pages 429-440 Non-Compact Lie Group Actions....Pages 441-445 Fixed Point Sets of Transformation Groups on Separable Infinite-Dimensional Frechet Spaces....Pages 446-450 On a Kind of Discrete Transformation Group....Pages 451-456