Odd Primary Infinite Families in Stable Homotopy Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 082182242X
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Odd Primary Infinite Families in Stable Homotopy Theory by : Ralph L. Cohen

Download or read book Odd Primary Infinite Families in Stable Homotopy Theory written by Ralph L. Cohen and published by American Mathematical Soc.. This book was released on 1981 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses issues with odd primary infinite families in stable homotopy theory.

Complex Cobordism and Stable Homotopy Groups of Spheres

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Author :
Publisher : American Mathematical Society
ISBN 13 : 1470472937
Total Pages : 417 pages
Book Rating : 4.4/5 (74 download)

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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 Society. This book was released on 2023-02-09 with total page 417 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.

Homotopy Theory via Algebraic Geometry and Group Representations

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821808052
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopy Theory via Algebraic Geometry and Group Representations by : Mark E. Mahowald

Download or read book Homotopy Theory via Algebraic Geometry and Group Representations written by Mark E. Mahowald and published by American Mathematical Soc.. This book was released on 1998 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.

Complex Cobordism and Stable Homotopy Groups of Spheres

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 082182967X
Total Pages : 418 pages
Book Rating : 4.8/5 (218 download)

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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.

Algebraic Topology

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821851624
Total Pages : 481 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Topology by : Martin C. Tangora

Download or read book Algebraic Topology written by Martin C. Tangora and published by American Mathematical Soc.. This book was released on 1993 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of twenty-nine articles contributed by participants of an International Conference in Algebraic Topology held in July 1991 in Oaxtepec, Mexico. In addition to papers on current research, there are several surveys and expositions on the work of Mark Mahowald, whose sixtieth birthday was celebrated during the conference. The conference was truly international, with over 130 mathematicians from fifteen countries. It ended with a spectacular total eclipse of the sun, a photograph of which appears as the frontispiece. The papers range over much of algebraic topology and cross over into related areas, such as $K$-theory, representation theory, and Lie groups. Also included is a chart of the Adams spectral sequence and a bibliography of Mahowald's publications.

Braids

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Publisher : American Mathematical Soc.
ISBN 13 : 0821850881
Total Pages : 730 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Braids by : Joan S. Birman

Download or read book Braids written by Joan S. Birman and published by American Mathematical Soc.. This book was released on 1988 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artin introduced braid groups into mathematical literature in 1925. In the years since, and particularly in the last five to ten years, braid groups have played diverse and unexpected roles in widely different areas of mathematics, including knot theory, homotopy theory, singularity theory, and dynamical systems. Most recently, the area of operator algebras has brought striking new applications to knots and links. This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This interdisciplinary conference brought together leading specialists in diverse areas of mathematics to discuss their discoveries and to exchange ideas and problems concerning this important and fundamental group. Because the proceedings present a mix of expository articles and new research, this volume will be of interest to graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area. The required background includes the basics of knot theory, group theory, and low-dimensional topology.

Nilpotence and Periodicity in Stable Homotopy Theory

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Author :
Publisher : Princeton University Press
ISBN 13 : 9780691025728
Total Pages : 228 pages
Book Rating : 4.0/5 (257 download)

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Book Synopsis Nilpotence and Periodicity in Stable Homotopy Theory by : Douglas C. Ravenel

Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Homotopy Invariant Algebraic Structures

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 082181057X
Total Pages : 392 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopy Invariant Algebraic Structures by : Jean-Pierre Meyer

Download or read book Homotopy Invariant Algebraic Structures written by Jean-Pierre Meyer and published by American Mathematical Soc.. This book was released on 1999 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.

Algebraic Topology and Algebraic K-Theory (AM-113), Volume 113

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Publisher : Princeton University Press
ISBN 13 : 1400882117
Total Pages : 567 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Algebraic Topology and Algebraic K-Theory (AM-113), Volume 113 by : William Browder

Download or read book Algebraic Topology and Algebraic K-Theory (AM-113), Volume 113 written by William Browder and published by Princeton University Press. This book was released on 2016-03-02 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains accounts of talks held at a symposium in honor of John C. Moore in October 1983 at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.

Algebraic Topology

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Publisher : Springer
ISBN 13 : 3540461604
Total Pages : 469 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic Topology by : Gunnar Carlsson

Download or read book Algebraic Topology written by Gunnar Carlsson and published by Springer. This book was released on 2006-11-14 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in part to mark the 25th anniversary of the journal Topology and 60th birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and was conceived as a successor to the Aarhus conferences of 1978 and 1982. Some thirty papers are included in this volume, mostly at a research level. Subjects include cyclic homology, H-spaces, transformation groups, real and rational homotopy theory, acyclic manifolds, the homotopy theory of classifying spaces, instantons and loop spaces, and complex bordism.

Proceedings of the Northwestern Homotopy Theory Conference

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821850202
Total Pages : 454 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Proceedings of the Northwestern Homotopy Theory Conference by : Haynes R. Miller

Download or read book Proceedings of the Northwestern Homotopy Theory Conference written by Haynes R. Miller and published by American Mathematical Soc.. This book was released on 1983 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Formal Geometry and Bordism Operations

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Publisher : Cambridge University Press
ISBN 13 : 1108428037
Total Pages : 421 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Formal Geometry and Bordism Operations by : Eric Peterson

Download or read book Formal Geometry and Bordism Operations written by Eric Peterson and published by Cambridge University Press. This book was released on 2019 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.

A User's Guide to Spectral Sequences

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Publisher : Cambridge University Press
ISBN 13 : 0521567599
Total Pages : 579 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis A User's Guide to Spectral Sequences by : John McCleary

Download or read book A User's Guide to Spectral Sequences written by John McCleary and published by Cambridge University Press. This book was released on 2001 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stable and Unstable Homotopy

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821871263
Total Pages : 328 pages
Book Rating : 4.8/5 (712 download)

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Book Synopsis Stable and Unstable Homotopy by : William G. Dwyer

Download or read book Stable and Unstable Homotopy written by William G. Dwyer and published by American Mathematical Soc.. This book was released on 1998-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.

Differential Geometry and Topology

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Publisher : Springer
ISBN 13 : 354046137X
Total Pages : 377 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Differential Geometry and Topology by : Boju Jiang

Download or read book Differential Geometry and Topology written by Boju Jiang and published by Springer. This book was released on 2006-11-14 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Primary Homotopy Theory

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821822322
Total Pages : 67 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Primary Homotopy Theory by : Joseph Neisendorfer

Download or read book Primary Homotopy Theory written by Joseph Neisendorfer and published by American Mathematical Soc.. This book was released on 1980 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author gives a systematic exposition of homotopy groups with coefficients in a cyclic group [italic]Z or [italic]Z[subscript italic]k. The text pays particular attention to low-dimensional cases and trouble with the small primes. The book gives a complete treatment of some topics--such as Samelson products--with a view toward applications.

Notices of the American Mathematical Society

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Publisher :
ISBN 13 :
Total Pages : 720 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Notices of the American Mathematical Society by : American Mathematical Society

Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1982 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: