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The Algebra Of Secondary Cohomology Operations And Its Dual
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Book Synopsis The Algebra of Secondary Cohomology Operations by : Hans-Joachim Baues
Download or read book The Algebra of Secondary Cohomology Operations written by Hans-Joachim Baues and published by Springer Science & Business Media. This book was released on 2006-06-12 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. This book computes the algebra of secondary cohomology operations which enriches the structure of the Steenrod algebra in a new and unexpected way. The book solves a long-standing problem on the algebra of secondary cohomology operations by developing a new algebraic theory of such operations. The results have strong impact on the Adams spectral sequence and hence on the computation of homotopy groups of spheres.
Book Synopsis Cohomology Operations and Applications in Homotopy Theory by : Robert E. Mosher
Download or read book Cohomology Operations and Applications in Homotopy Theory written by Robert E. Mosher and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Book Synopsis Secondary Cohomology Operations by : John R. Harper
Download or read book Secondary Cohomology Operations written by John R. Harper and published by American Mathematical Soc.. This book was released on 2002 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS now fills that gap with the publication of the present volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among manyapplications considered are the Hopf invariant one theorem (for all primes $p$, including $p = 2$), Browder's theorem on higher Bockstein operations, and cohomology theory of Massey-Peterson fibrations. Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary ofmore advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations. The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.
Book Synopsis Complex Cobordism and Stable Homotopy Groups of Spheres by : Douglas C. Ravenel
Download or read book Complex Cobordism and Stable Homotopy Groups of Spheres written by Douglas C. Ravenel and published by American Mathematical Soc.. This book was released on 2003-11-25 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Book Synopsis The Factorization of Cyclic Reduced Powers by Secondary Cohomology Operations by : Arunas Liulevicius
Download or read book The Factorization of Cyclic Reduced Powers by Secondary Cohomology Operations written by Arunas Liulevicius and published by American Mathematical Soc.. This book was released on 1962 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polynomials and the mod 2 Steenrod Algebra by : Grant Walker
Download or read book Polynomials and the mod 2 Steenrod Algebra written by Grant Walker and published by Cambridge University Press. This book was released on 2018 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
Book Synopsis Polynomials and the mod 2 Steenrod Algebra by : Grant Walker (Mathematician)
Download or read book Polynomials and the mod 2 Steenrod Algebra written by Grant Walker (Mathematician) and published by Cambridge University Press. This book was released on 2018 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Book Synopsis The Selected Works of J. Frank Adams: Volume 2 by : John Frank Adams
Download or read book The Selected Works of J. Frank Adams: Volume 2 written by John Frank Adams and published by Cambridge University Press. This book was released on 1992-10-07 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selected works of one the greatest names in algebraic topology.
Book Synopsis Introduction to Homotopy Theory by : Paul Selick
Download or read book Introduction to Homotopy Theory written by Paul Selick and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Book Synopsis Current Trends in Algebraic Topology by : Richard M. Kane
Download or read book Current Trends in Algebraic Topology written by Richard M. Kane and published by American Mathematical Soc.. This book was released on 1982-01-01 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a Conference held at the University of Western Ontario in 1981. More than one hundred papers were presented by researchers from a wide spectrum of countries and institutions.
Book Synopsis Illinois Journal of Mathematics by :
Download or read book Illinois Journal of Mathematics written by and published by . This book was released on 1993 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Developments in Topology by : John Frank Adams
Download or read book New Developments in Topology written by John Frank Adams and published by Cambridge University Press. This book was released on 1974-02-28 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in June 1972 have revised their contributions and submitted them for publication in this volume. The present papers do not necessarily closely correspond with the original talks, as it was the intention of the volume editor to make this book of mathematical rather than historical interest. The contributions will be of value to workers in topology in universities and polytechnics.
Book Synopsis Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) by : Grant Walker
Download or read book Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) written by Grant Walker and published by Cambridge University Press. This book was released on 2017-11-09 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Book Synopsis The Selected Works of J. Frank Adams by : John Frank Adams
Download or read book The Selected Works of J. Frank Adams written by John Frank Adams and published by Cambridge University Press. This book was released on 1992-10-07 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selected works of one the greatest names in algebraic topology.
Download or read book Pacific Journal of Mathematics written by and published by . This book was released on 1987-05 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry and Topology by : Jacob Palis
Download or read book Geometry and Topology written by Jacob Palis and published by Springer. This book was released on 2006-11-15 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: III. Latin American School of Mathematics
Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
