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Author : Grant Walker,Reginald M. W. Wood
Publisher : Cambridge University Press
Page : 371 pages
File Size : 54,5 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9781108414487
The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
Author : Grant Walker,Reginald M. W. Wood
Publisher : Cambridge University Press
Page : 381 pages
File Size : 49,8 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9781108414456
The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.
Author : Grant Walker (Mathematician),Reginald M. W. Wood
Publisher : Unknown
Page : 128 pages
File Size : 44,6 Mb
Release : 2018
Category : Polynomials
ISBN : OCLC:1015730861
Author : Grant Walker,Reginald M. W. Wood
Publisher : Cambridge University Press
Page : 381 pages
File Size : 45,7 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9781108355926
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.
Author : Grant Walker (Mathematician),Reginald M. W. Wood
Publisher : Unknown
Page : 128 pages
File Size : 40,9 Mb
Release : 2018
Category : Polynomials
ISBN : OCLC:1015730861
Author : Douglas C. Ravenel
Publisher : American Mathematical Society
Page : 417 pages
File Size : 44,5 Mb
Release : 2023-02-09
Category : Mathematics
ISBN : 9781470472931
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 : Anonim
Publisher : Unknown
Page : 678 pages
File Size : 53,5 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015028388760
Author : Mahender Singh,Yongjin Song,Jie Wu
Publisher : Springer
Page : 313 pages
File Size : 40,5 Mb
Release : 2019-02-02
Category : Mathematics
ISBN : 9789811357428
This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.
Author : Robert R. Bruner,J. Peter May,James E. McClure,Mark Steinberger
Publisher : Springer
Page : 396 pages
File Size : 51,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540397786
Author : John Willard Milnor
Publisher : Unknown
Page : 326 pages
File Size : 43,7 Mb
Release : 1959
Category : Topology
ISBN : UOM:39015095249416
Author : Bjorn Ian Dundas,Marc Levine,P.A. Østvær,Oliver Röndigs,Vladimir Voevodsky
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 52,9 Mb
Release : 2007-07-11
Category : Mathematics
ISBN : 9783540458975
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Author : F. R. Cohen,T. J. Lada,P. J. May
Publisher : Springer
Page : 501 pages
File Size : 46,5 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540379850
Author : Dagmar M. Meyer,Larry Smith
Publisher : Cambridge University Press
Page : 210 pages
File Size : 47,7 Mb
Release : 2005-08-18
Category : Mathematics
ISBN : 0521850649
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Author : Dennis P. Sullivan
Publisher : Springer
Page : 286 pages
File Size : 47,9 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 9048103509
The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.
Author : Haynes R Miller
Publisher : World Scientific
Page : 405 pages
File Size : 46,6 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9789811231261
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.