Download or read book Polynomials and the mod 2 Steenrod Algebra written by Grant Walker and published by Cambridge University Press. This book was released on 2018 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
Download or read book Polynomials and the mod 2 Steenrod Algebra written by Grant Walker (Mathematician) and published by Cambridge University Press. This book was released on 2018 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Download or read book Polynomials and the mod 2 Steenrod Algebra Volume 2 Representations of GL n F2 written by Grant Walker and published by Cambridge University Press. This book was released on 2017-11-09 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
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.
Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1997 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Characteristic Classes written by John Willard Milnor and published by . This book was released on 1959 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vietnam Journal of Mathematics written by and published by . This book was released on 2003 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book H Ring Spectra and Their Applications written by Robert R. Bruner and published by Springer. This book was released on 2006-11-14 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Homology of Iterated Loop Spaces written by F. R. Cohen and published by Springer. This book was released on 2007-01-05 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Lectures On Algebraic Topology written by Haynes R Miller and published by World Scientific. This book was released on 2021-09-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Download or read book Algebraic Methods in Unstable Homotopy Theory written by Joseph Neisendorfer and published by Cambridge University Press. This book was released on 2010-02-18 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Homology of Linear Groups written by Kevin P. Knudson and published by Springer Science & Business Media. This book was released on 2000-12-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation. It presents the stability theorems and low-dimensional results of A. Suslin, W. van der Kallen and others are presented. Coverage also examines the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete.
Download or read book Topological Modular Forms written by Christopher L. Douglas and published by American Mathematical Soc.. This book was released on 2014-12-04 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
