The Factorization Of Cyclic Reduced Powers By Secondary Cohomology Operations
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The Factorization Of Cyclic Reduced Powers By Secondary Cohomology Operations
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Author : Arunas Liulevicius
language : en
Publisher: American Mathematical Soc.
Release Date : 1962
The Factorization Of Cyclic Reduced Powers By Secondary Cohomology Operations written by Arunas Liulevicius and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Algebraic topology categories.
The Algebra Of Secondary Cohomology Operations
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Author : Hans-Joachim Baues
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-12
The Algebra Of Secondary Cohomology Operations written by Hans-Joachim Baues and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-12 with Mathematics categories.
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.
Secondary Cohomology Operations
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Author : John R. Harper
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Secondary Cohomology Operations written by John R. Harper and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Homology theory categories.
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.
Odd Primary Infinite Families In Stable Homotopy Theory
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Author : Ralph L. Cohen
language : en
Publisher: American Mathematical Soc.
Release Date : 1981
Odd Primary Infinite Families In Stable Homotopy Theory written by Ralph L. Cohen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Adams spectral sequences categories.
Addresses issues with odd primary infinite families in stable homotopy theory.
Steenrod Squares In Spectral Sequences
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Author : William M. Singer
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Steenrod Squares In Spectral Sequences written by William M. Singer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Spectral sequences (Mathematics). categories.
This book develops a general theory of Steenrod operations in spectral sequences. It gives special attention to the change-of-rings spectral sequence for the cohomology of an extension of Hopf algebras and to the Eilenberg-Moore spectral sequence for the cohomology of classifying spaces and homotopy orbit spaces. In treating the change-of-rings spectral sequence, the book develops from scratch the necessary properties of extensions of Hopf algebras and constructs the spectral sequence in a form particularly suited to the introduction of Steenrod squares. The resulting theory can be used effectively for the computation of the cohomology rings of groups and Hopf algebras, and of the Steenrod algebra in particular, and so should play a useful role in stable homotopy theory. Similarly the book offers a self-contained construction of the Eilenberg-Moore spectral sequence, in a form suitable for the introduction of Steenrod operations. The corresponding theory is an effective tool for the computation of t
Polynomials And The Mod 2 Steenrod Algebra
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Author : Grant Walker
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-09
Polynomials And The Mod 2 Steenrod Algebra written by Grant Walker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
Polynomials And The Mod 2 Steenrod Algebra
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Author : Grant Walker
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-09
Polynomials And The Mod 2 Steenrod Algebra written by Grant Walker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.
Lie Algebras And Lie Groups
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1955
Lie Algebras And Lie Groups written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with Lie algebras categories.
The American Mathematical Society, with the financial support of the National Science Foundation, held its First Summer Mathematical Institute from June 20 to July 31, 1953. The topic chosen was Lie theory, twenty-nine mathematicians active in this area attended. The six-week period provided opportunity both for the interchange of ideas and for the subsequent shaping of ideas into theorems. The five papers present some results achieved by the participants.--Foreword.
The Adams Spectral Sequence For Topological Modular Forms
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Author : Robert R. Bruner
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-23
The Adams Spectral Sequence For Topological Modular Forms written by Robert R. Bruner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-23 with Mathematics categories.
The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.
Algebraic Methods In Unstable Homotopy Theory
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Author : Joseph Neisendorfer
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-18
Algebraic Methods In Unstable Homotopy Theory written by Joseph Neisendorfer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-18 with Mathematics categories.
The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.