Cohomology Theory Of Topological Transformation Groups

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Cohomology Theory of Topological Transformation Groups

Author : W.Y. Hsiang
Publisher : Springer Science & Business Media
ISBN 13 : 3642660525
Total Pages : 175 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Cohomology Theory of Topological Transformation Groups by : W.Y. Hsiang

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.

Cohomological Methods in Transformation Groups

Author : C. Allday
Publisher : Cambridge University Press
ISBN 13 : 0521350220
Total Pages : 486 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Cohomological Methods in Transformation Groups by : C. Allday

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.

Transformation Groups and Representation Theory

Author : T. Tom Dieck
Publisher : Springer
ISBN 13 : 3540385177
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Transformation Groups and Representation Theory by : T. Tom Dieck

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:

Transformation Groups

Author : Goutam Mukherjee
Publisher : Springer
ISBN 13 : 9386279304
Total Pages : 140 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Transformation Groups by : Goutam Mukherjee

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.

Transformation Groups

Author : Tammo tom Dieck
Publisher : Walter de Gruyter
ISBN 13 : 3110858371
Total Pages : 325 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Transformation Groups by : Tammo tom Dieck

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

Introduction to Compact Transformation Groups

Author :
Publisher : Academic Press
ISBN 13 : 9780080873596
Total Pages : 458 pages
Book Rating : 4.8/5 (735 download)

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Book Synopsis Introduction to Compact Transformation Groups by :

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 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Compact Transformation Groups

Cohomology of Groups

Author : Kenneth S. Brown
Publisher : Springer Science & Business Media
ISBN 13 : 1468493272
Total Pages : 318 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Cohomology of Groups by : Kenneth S. Brown

Download or read book Cohomology of Groups written by Kenneth S. Brown and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

Cohomology Theories for Compact Abelian Groups

Author : Karl H. Hofmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642806708
Total Pages : 235 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Cohomology Theories for Compact Abelian Groups by : Karl H. Hofmann

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.

Algebraic Topology and Transformation Groups

Author : Tammo tom Dieck
Publisher : Springer
ISBN 13 : 3540460365
Total Pages : 311 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic Topology and Transformation Groups by : Tammo tom Dieck

Download or read book Algebraic Topology and Transformation Groups written by Tammo tom Dieck and published by Springer. This book was released on 2006-11-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Equivariant Homotopy and Cohomology Theory

Author : J. Peter May
Publisher : American Mathematical Soc.
ISBN 13 : 0821803190
Total Pages : 366 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Equivariant Homotopy and Cohomology Theory by : J. Peter May

Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 1996 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. It then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology.Finally, the book gives an introduction to 'brave new algebra', the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail. It introduces many of the fundamental ideas and concepts of modern algebraic topology. It presents comprehensive material not found in any other book on the subject. It provides a coherent overview of many areas of current interest in algebraic topology. It surveys a great deal of material, explaining main ideas without getting bogged down in details.

Proceedings of the Conference on Transformation Groups

Author : P. S. Mostert
Publisher : Springer Science & Business Media
ISBN 13 : 3642461417
Total Pages : 470 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Proceedings of the Conference on Transformation Groups by : P. S. Mostert

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.

Algebraic Topology

Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
ISBN 13 : 1468493221
Total Pages : 548 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Algebraic Topology by : Edwin H. Spanier

Download or read book Algebraic Topology written by Edwin H. Spanier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Seminar on Transformation Groups

Author : Armand Borel
Publisher : Princeton University Press
ISBN 13 : 9780691090948
Total Pages : 262 pages
Book Rating : 4.0/5 (99 download)

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Book Synopsis Seminar on Transformation Groups by : Armand Borel

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 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar on Transformation Groups. (AM-46), Volume 46, will be forthcoming.

Cohomology Theories

Author : Eldon Dyer
Publisher :
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Cohomology Theories by : Eldon Dyer

Download or read book Cohomology Theories written by Eldon Dyer and published by . This book was released on 1969 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Equivariant Cohomology Theories

Author : Glen E. Bredon
Publisher : Springer
ISBN 13 : 3540349731
Total Pages : 72 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Equivariant Cohomology Theories by : Glen E. Bredon

Download or read book Equivariant Cohomology Theories written by Glen E. Bredon and published by Springer. This book was released on 2006-11-14 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: a

Algebraic Topology and Related Topics

Author : Mahender Singh
Publisher : Springer
ISBN 13 : 9811357420
Total Pages : 313 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Algebraic Topology and Related Topics by : Mahender Singh

Download or read book Algebraic Topology and Related Topics written by Mahender Singh and published by Springer. This book was released on 2019-02-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.

Topological Methods in Group Theory

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
ISBN 13 : 0387746110
Total Pages : 473 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Topological Methods in Group Theory by : Ross Geoghegan

Download or read book Topological Methods in Group Theory written by Ross Geoghegan and published by Springer Science & Business Media. This book was released on 2007-12-17 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.