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Author : P. E. Conner
Publisher : Springer
ISBN 13 : 3540699740
Total Pages : 120 pages
Book Rating : 4.5/5 (46 download)
Download or read book The Relation of Cobordism to K-Theories written by P. E. Conner and published by Springer. This book was released on 2006-11-14 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert E. Stong
Publisher : Princeton University Press
ISBN 13 : 1400879973
Total Pages : 421 pages
Book Rating : 4.4/5 (8 download)
Download or read book Notes on Cobordism Theory written by Robert E. Stong and published by Princeton University Press. This book was released on 2015-12-08 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes contain the first complete treatment of cobordism, a topic that has become increasingly important in the past ten years. The subject is fully developed and the latest theories are treated. Originally published in 1968. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Marc Levine
Publisher : Springer Science & Business Media
ISBN 13 : 3540368248
Total Pages : 252 pages
Book Rating : 4.5/5 (43 download)
Download or read book Algebraic Cobordism written by Marc Levine and published by Springer Science & Business Media. This book was released on 2007-02-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.
Author : Nigel Ray
Publisher : American Mathematical Soc.
ISBN 13 : 0821821938
Total Pages : 80 pages
Book Rating : 4.8/5 (218 download)
Download or read book Normal Structures and Bordism Theory, with Applications to $MSp_\ast $ written by Nigel Ray and published by American Mathematical Soc.. This book was released on 1977 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first of these three papers we discuss the problem of enumerating the bordism classes which can be carried on a fixed manifold by means of varying its normal structure. The main application is to Sp structures on Alexander's family of manifolds, and is presented in the third paper. The middle paper collects together the requisite definitions and calculations.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1974-02 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yu. B. Rudyak
Publisher : Springer Science & Business Media
ISBN 13 : 3540777512
Total Pages : 593 pages
Book Rating : 4.5/5 (47 download)
Download or read book On Thom Spectra, Orientability, and Cobordism written by Yu. B. Rudyak and published by Springer Science & Business Media. This book was released on 2007-12-12 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.
Author : Douglas C. Ravenel
Publisher : American Mathematical Soc.
ISBN 13 : 082182967X
Total Pages : 418 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Max Karoubi
Publisher : Springer Science & Business Media
ISBN 13 : 3540798900
Total Pages : 337 pages
Book Rating : 4.5/5 (47 download)
Download or read book K-Theory written by Max Karoubi and published by Springer Science & Business Media. This book was released on 2009-11-27 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Author : Wayne Raskind
Publisher : American Mathematical Soc.
ISBN 13 : 082180927X
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic $K$-Theory written by Wayne Raskind and published by American Mathematical Soc.. This book was released on 1999 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the Joint Summer Research Conference on Algebraic K-theory held at the University of Washington in Seattle. High-quality surveys are written by leading experts in the field. Included is an up-to-date account of Voevodsky's proof of the Milnor conjecture relating the Milnor K-theory of fields to Galois cohomology. The book is intended for graduate students and research mathematicians interested in $K$-theory, algebraic geometry, and number theory.
Author : Idar Hansen
Publisher :
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.X/5 (1 download)
Download or read book On Complex Cobordism Theory written by Idar Hansen and published by . This book was released on 1974 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Serguei Petrovich Novikov
Publisher : World Scientific
ISBN 13 : 9814475955
Total Pages : 386 pages
Book Rating : 4.8/5 (144 download)
Download or read book Topological Library - Part 1: Cobordisms And Their Applications written by Serguei Petrovich Novikov and published by World Scientific. This book was released on 2007-07-09 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three volumes collecting the original and now classic works in topology written in the 50s-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 fibre spaces.”This is the translation of the Russian edition published in 2005 with one entry (Milnor's lectures on the h-cobordism) omitted.
Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 0821805029
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)
Download or read book Moment Maps, Cobordisms, and Hamiltonian Group Actions written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
Author : John Frank Adams
Publisher : University of Chicago Press
ISBN 13 : 0226005240
Total Pages : 384 pages
Book Rating : 4.2/5 (26 download)
Download or read book Stable Homotopy and Generalised Homology written by John Frank Adams and published by University of Chicago Press. This book was released on 1974 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Author : John Milnor
Publisher : Princeton University Press
ISBN 13 : 140088182X
Total Pages : 340 pages
Book Rating : 4.4/5 (8 download)
Download or read book Characteristic Classes. (AM-76), Volume 76 written by John Milnor and published by Princeton University Press. This book was released on 2016-03-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Author : John Willard Milnor
Publisher : Princeton University Press
ISBN 13 : 9780691081229
Total Pages : 342 pages
Book Rating : 4.0/5 (812 download)
Download or read book Characteristic Classes written by John Willard Milnor and published by Princeton University Press. This book was released on 1974 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Author : Gunnar Carlsson
Publisher : Springer
ISBN 13 : 3540461604
Total Pages : 469 pages
Book Rating : 4.5/5 (44 download)
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.
Author : Nigel Ray
Publisher : Cambridge University Press
ISBN 13 : 0521421535
Total Pages : 333 pages
Book Rating : 4.5/5 (214 download)
Download or read book Adams Memorial Symposium on Algebraic Topology written by Nigel Ray and published by Cambridge University Press. This book was released on 1992 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the symposium; the articles contained here range from overviews to reports of work still in progress, as well as a survey and complete bibliography of Adams' own work. These proceedings form an important compendium of current research in algebraic topology, and.
