Download or read book Cohomology Theory of Topological Transformation Groups written by W.Y. Hsiang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L. E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or non-existence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P. A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups.
Download or read book Cohomology Theory of Compact Transformation Groups written by Tor Skjelbred and published by . This book was released on 1972 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Compact Transformation Groups written by and published by Academic Press. This book was released on 1972-09-29 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Compact Transformation Groups
Download or read book Cohomological Methods in Transformation Groups written by C. Allday and published by Cambridge University Press. This book was released on 1993-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
Download or read book Transformation Groups and Representation Theory written by T. Tom Dieck and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cohomology Theories for Compact Abelian Groups written by Karl H. Hofmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two.
Download or read book Seminar on Transformation Groups written by Armand Borel and published by Princeton University Press. This book was released on 1960 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Armond Borel’s influential seminar on transformation groups from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Download or read book Cohomology theory of topological transformation groups written by Wu Yi Hsiang and published by . This book was released on 1975 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transformation Groups and Algebraic K Theory written by Wolfgang Lück and published by Springer. This book was released on 2006-11-14 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Download or read book Transformation Groups written by Tammo tom Dieck and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This book is a jewel – it explains important, useful and deep topics in Algebraic Topology that you won’t find elsewhere, carefully and in detail.” Prof. Günter M. Ziegler, TU Berlin
Download or read book Cohomology Structure of Compact Transformation Groups written by Hsu-Tung Ku and published by . This book was released on 1967 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Continuous Bounded Cohomology of Locally Compact Groups written by Nicolas Monod and published by Springer. This book was released on 2003-07-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.
Download or read book Transformation Groups written by Goutam Mukherjee and published by Springer. This book was released on 2005-04-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed lectures presented earlier at Winter School on Transformation Groups.
Download or read book Cohomology Theories for Compact Abelian Groups written by Eric C Nummela and published by . This book was released on 1974-04-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Conference on Transformation Groups written by P. S. Mostert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cohomology Theories for Compact Abelian Groups written by Karl Heinrich Hofmann and published by . This book was released on 1973 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Splitting Principle of Cohomology Theory of Transformation Groups written by Theodore Ching-Chien Chang and published by . This book was released on 1972 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
