A Users Guide To Spectral Sequences PDF Download
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Author | : John McCleary |
Publisher | : Cambridge University Press |
Total Pages | : 579 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0521567599 |
Download A User's Guide to Spectral Sequences Book in PDF, ePub and Kindle
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 | : John McCleary |
Publisher | : Cambridge University Press |
Total Pages | : 578 |
Release | : 2000-11-27 |
Genre | : Mathematics |
ISBN | : 9780521567596 |
Download A User's Guide to Spectral Sequences Book in PDF, ePub and Kindle
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 | : John McCleary |
Publisher | : |
Total Pages | : |
Release | : 2010-07-23 |
Genre | : |
ISBN | : 9780521169974 |
Download A User's Guide to Spectral Sequences ICM Edition Book in PDF, ePub and Kindle
Author | : Stanley O. Kochman |
Publisher | : American Mathematical Soc. |
Total Pages | : 294 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9780821806005 |
Download Bordism, Stable Homotopy and Adams Spectral Sequences Book in PDF, ePub and Kindle
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. All results are proved in complete detail. Only elementary facts from algebraic topology and homological algebra are assumed. Each chapter concludes with a guide for further study.
Author | : J. P. May |
Publisher | : University of Chicago Press |
Total Pages | : 262 |
Release | : 1999-09 |
Genre | : Mathematics |
ISBN | : 9780226511832 |
Download A Concise Course in Algebraic Topology Book in PDF, ePub and Kindle
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author | : Michael Atiyah |
Publisher | : CRC Press |
Total Pages | : 181 |
Release | : 2018-03-05 |
Genre | : Mathematics |
ISBN | : 0429973179 |
Download K-theory Book in PDF, ePub and Kindle
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.
Author | : John McCleary |
Publisher | : Cambridge University Press |
Total Pages | : 375 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 0521116074 |
Download Geometry from a Differentiable Viewpoint Book in PDF, ePub and Kindle
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Author | : Ravindran Kannan |
Publisher | : Now Publishers Inc |
Total Pages | : 153 |
Release | : 2009 |
Genre | : Computers |
ISBN | : 1601982747 |
Download Spectral Algorithms Book in PDF, ePub and Kindle
Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
Author | : Haynes R Miller |
Publisher | : World Scientific |
Total Pages | : 405 |
Release | : 2021-09-20 |
Genre | : Mathematics |
ISBN | : 9811231265 |
Download Lectures On Algebraic Topology Book in PDF, ePub and Kindle
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 | : Grant Heiken |
Publisher | : CUP Archive |
Total Pages | : 796 |
Release | : 1991-04-26 |
Genre | : Science |
ISBN | : 9780521334440 |
Download Lunar Sourcebook Book in PDF, ePub and Kindle
The only work to date to collect data gathered during the American and Soviet missions in an accessible and complete reference of current scientific and technical information about the Moon.