Steenrod Squares In Spectral Sequences

Author : William M. Singer
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 42,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821841419

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Steenrod Squares in Spectral Sequences by William M. Singer Pdf

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

Author : S P Novikov,I A Taimanov
Publisher : World Scientific
Page : 592 pages
File Size : 53,7 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9789814401326

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Topological Library by S P Novikov,I A Taimanov Pdf

The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s–1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.” Contents:Singular Homology of Fiber Spaces (J-P Serre)Homotopy Groups and Classes of Abelian Groups (J-P Serre)Cohomology Modulo 2 of Eilenberg–MacLane Complexes (J-P Serre)On Cohomology of Principal Fiber Bundles and Homogeneous Spaces of Compact Lie Groups (A Borel)Cohomology Mod 2 of Some Homogeneous Spaces (A Borel)The Steenrod Algebra and Its Dual (J Milnor)On the Structure and Applications of the Steenrod Algebra (J F Adams)Vector Bundles and Homogeneous Spaces (M F Atiyah and F Hirzebruch)The Methods of Algebraic Topology from Viewpoint of Cobordism Theory (S P Novikov) Readership: Researchers in algebraic topology, its applications, and history of topology. Keywords:Topology;Homeomorphism;Fundamental Group;Smooth Manifold;Homology;Homotopy;Fiber Spaces;Vector Bundles;Characteristic Classes;Homogeneous Spaces;Cobordism;Steenrod AlgebraKey Features:Serves as a tool in learning classical algebraic topologyAn essential book for topologistsReviews: "It is utmost useful to have these (interrelated) classics gathered together in one volume. This facilitates the study of the originals considerably, all the more as numerous editorial hints provide additional guidance. In this regard, the entire edition represents an invaluable source book for both students and researchers in the field." Zentralblatt MATH "This is a nice volume that should not be missing in any Mathematics Library." European Mathematical Society

Author : John McCleary
Publisher : Unknown
Page : 448 pages
File Size : 54,7 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015038861103

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User's Guide to Spectral Sequences by John McCleary Pdf

Author : John McCleary
Publisher : Cambridge University Press
Page : 579 pages
File Size : 49,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9780521567596

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A User's Guide to Spectral Sequences by John McCleary Pdf

Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Author : Stanley O. Kochman
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 50,8 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 9780821871904

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Bordism, Stable Homotopy, and Adams Spectral Sequences by Stanley O. Kochman Pdf

This book is a compilation of lecture notes that were prepared for the graduate course "Adams Spectral Sequences and Stable Homotopy Theory" given at The Fields Institute during the fall of 1995. The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems. Suitable as a text for an intermediate course in algebraic topology, this book provides a direct exposition of the basic concepts of bordism, characteristic classes, Adams spectral sequences, Brown-Peterson spectra and the computation of stable stems. The key ideas are presented in complete detail without becoming encyclopedic. The approach to characteristic classes and some of the methods for computing stable stems have not been published previously.

Author : Robert R. Bruner,John Rognes
Publisher : American Mathematical Society
Page : 690 pages
File Size : 47,7 Mb
Release : 2021-12-23
Category : Mathematics
ISBN : 9781470469580

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The Adams Spectral Sequence for Topological Modular Forms by Robert R. Bruner,John Rognes Pdf

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.

Author : Larry Smith
Publisher : Springer
Page : 149 pages
File Size : 53,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540362869

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Lectures on the Eilenberg-Moore Spectral Sequence by Larry Smith Pdf

Author : Robert E. Mosher,Martin C. Tangora
Publisher : Courier Corporation
Page : 226 pages
File Size : 52,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486466644

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Cohomology Operations and Applications in Homotopy Theory by Robert E. Mosher,Martin C. Tangora Pdf

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.

Author : D. Benson
Publisher : Springer
Page : 246 pages
File Size : 47,7 Mb
Release : 2008-07-22
Category : Mathematics
ISBN : 9783540389408

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Modular Representation Theory by D. Benson Pdf

This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.

Author : Serge? Petrovich Novikov
Publisher : World Scientific
Page : 590 pages
File Size : 55,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814401319

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Topological Library by Serge? Petrovich Novikov Pdf

The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in 1950-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated "singular homologies of fiber spaces."

Author : Anonim
Publisher : Unknown
Page : 520 pages
File Size : 41,9 Mb
Release : 1974
Category : Mathematical reviews
ISBN : UOM:39015016353685

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Index of Mathematical Papers by Anonim Pdf

Author : S.P. Novikov
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 51,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662105795

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Topology I by S.P. Novikov Pdf

This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.

Author : Haynes R Miller
Publisher : World Scientific
Page : 405 pages
File Size : 45,8 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9789811231261

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Lectures On Algebraic Topology by Haynes R Miller Pdf

Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.

Author : Anonim
Publisher : Unknown
Page : 804 pages
File Size : 48,8 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588624

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Mathematical Reviews by Anonim Pdf

Author : Douglas C. Ravenel
Publisher : American Mathematical Society
Page : 417 pages
File Size : 47,6 Mb
Release : 2023-02-09
Category : Mathematics
ISBN : 9781470472931

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Complex Cobordism and Stable Homotopy Groups of Spheres by Douglas C. Ravenel Pdf

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.