Unstable Modules Over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture

Unstable Modules Over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture PDF

Author: Lionel Schwartz

Publisher: University of Chicago Press

Published: 1994-07-15

Total Pages: 244

ISBN-13: 9780226742038

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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.

Polynomials and the mod 2 Steenrod Algebra

Polynomials and the mod 2 Steenrod Algebra PDF

Author: Grant Walker

Publisher: Cambridge University Press

Published: 2017-11-09

Total Pages: 381

ISBN-13: 1108414451

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The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.

Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)

Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) PDF

Author: Grant Walker

Publisher: Cambridge University Press

Published: 2017-11-09

Total Pages: 381

ISBN-13: 1108355927

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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.

Infinite Length Modules

Infinite Length Modules PDF

Author: Henning Krause

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 437

ISBN-13: 3034884265

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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.

Group Representations: Cohomology, Group Actions and Topology

Group Representations: Cohomology, Group Actions and Topology PDF

Author: Alejandro Adem

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 549

ISBN-13: 0821806580

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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.

Cohomological Methods in Homotopy Theory

Cohomological Methods in Homotopy Theory PDF

Author: Jaume Aguade

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 413

ISBN-13: 3034883129

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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.

Algebraic Topology

Algebraic Topology PDF

Author: H.V. Hưng Nguyễn

Publisher: Springer

Published: 2018-01-02

Total Pages: 180

ISBN-13: 3319694340

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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.

Homotopy Theoretic Methods in Group Cohomology

Homotopy Theoretic Methods in Group Cohomology PDF

Author: William G. Dwyer

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 106

ISBN-13: 3034883560

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This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.

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