Unstable Modules Over The Steenrod Algebra And Sullivans Fixed Point Set Conjecture

Author : Lionel Schwartz
Publisher : University of Chicago Press
ISBN 13 : 9780226742038
Total Pages : 244 pages
Book Rating : 4.32/5 ( download)

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Download or read book Unstable Modules Over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture written by Lionel Schwartz and published by University of Chicago Press. This book was released on 1994-07-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of one of the main directions of algebraic topology, this book focuses on the Sullivan conjecture and its generalizations and applications. Lionel Schwartz collects here for the first time some of the most innovative work on the theory of modules over the Steenrod algebra, including ideas on the Segal conjecture, work from the late 1970s by Adams and Wilkerson, and topics in algebraic group representation theory. This course-tested book provides a valuable reference for algebraic topologists and includes foundational material essential for graduate study.

Author : Grant Walker (Mathematician)
Publisher : Cambridge University Press
ISBN 13 : 1108414451
Total Pages : 381 pages
Book Rating : 4.56/5 ( download)

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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.

Author : Grant Walker
Publisher : Cambridge University Press
ISBN 13 : 1108414486
Total Pages : 371 pages
Book Rating : 4.87/5 ( download)

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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.

Author : Grant Walker
Publisher : Cambridge University Press
ISBN 13 : 1108355927
Total Pages : 381 pages
Book Rating : 4.26/5 ( download)

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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.

Author : Henning Krause
Publisher : Birkhäuser
ISBN 13 : 3034884265
Total Pages : 437 pages
Book Rating : 4.66/5 ( download)

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Download or read book Infinite Length Modules written by Henning Krause and published by Birkhäuser. This book was released on 2012-12-06 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the role played by modules of infinite length when dealing with problems in the representation theory of groups and algebras, but also in topology and geometry; it shows the intriguing interplay between finite and infinite length modules.

Author : Alejandro Adem
Publisher : American Mathematical Soc.
ISBN 13 : 0821806580
Total Pages : 549 pages
Book Rating : 4.86/5 ( download)

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Download or read book Group Representations: Cohomology, Group Actions and Topology written by Alejandro Adem and published by American Mathematical Soc.. This book was released on 1998 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.

Author : Jaume Aguade
Publisher : Birkhäuser
ISBN 13 : 3034883129
Total Pages : 413 pages
Book Rating : 4.22/5 ( download)

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Download or read book Cohomological Methods in Homotopy Theory written by Jaume Aguade and published by Birkhäuser. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.

Author : H.V. Hưng Nguyễn
Publisher : Springer
ISBN 13 : 3319694340
Total Pages : 187 pages
Book Rating : 4.44/5 ( download)

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Download or read book Algebraic Topology written by H.V. Hưng Nguyễn and published by Springer. This book was released on 2018-01-02 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G. Ginot, H.-W. Henn and G. Powell. They are all introductory texts and can be used by PhD students and experts in the field. Among the three contributions, two concern stable homotopy of spheres: Henn focusses on the chromatic point of view, the Morava K(n)-localization and the cohomology of the Morava stabilizer groups. Powell’s chapter is concerned with the derived functors of the destabilization and iterated loop functors and provides a small complex to compute them. Indications are given for the odd prime case. Providing an introduction to some aspects of string and brane topology, Ginot’s contribution focusses on Hochschild homology and its generalizations. It contains a number of new results and fills a gap in the literature.

Author : Douglas C. Ravenel
Publisher : American Mathematical Society
ISBN 13 : 1470472937
Total Pages : 417 pages
Book Rating : 4.31/5 ( download)

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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.

Author : Dagmar M. Meyer
Publisher : Cambridge University Press
ISBN 13 : 9780521850643
Total Pages : 210 pages
Book Rating : 4.49/5 ( download)

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Download or read book Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations written by Dagmar M. Meyer and published by Cambridge University Press. This book was released on 2005-08-18 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.