Homotopy Theoretic Methods In Group Cohomology PDF Download
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| Author | : William G. Dwyer |
| Publisher | : Birkhäuser |
| Total Pages | : 106 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883560 |
Download Homotopy Theoretic Methods in Group Cohomology Book in PDF, ePub and Kindle
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.
| Author | : Alejandro Adem |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803050 |
Download Homotopy Theory and Its Applications Book in PDF, ePub and Kindle
This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.
| Author | : Nicholas Kuhn |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 370 |
| Release | : 2001-04-25 |
| Genre | : Mathematics |
| ISBN | : 0821826212 |
Download Homotopy Methods in Algebraic Topology Book in PDF, ePub and Kindle
This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.
| Author | : Robert E. Mosher |
| Publisher | : Courier Corporation |
| Total Pages | : 226 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486466647 |
Download Cohomology Operations and Applications in Homotopy Theory Book in PDF, ePub and Kindle
Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
| Author | : Alejandro Adem |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662062828 |
Download Cohomology of Finite Groups Book in PDF, ePub and Kindle
The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.
| Author | : Meinolf Geck |
| Publisher | : EPFL Press |
| Total Pages | : 472 |
| Release | : 2007-05-07 |
| Genre | : Mathematics |
| ISBN | : 9780849392436 |
Download Group Representation Theory Book in PDF, ePub and Kindle
After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).
| Author | : Ross Geoghegan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 473 |
| Release | : 2007-12-17 |
| Genre | : Mathematics |
| ISBN | : 0387746110 |
Download Topological Methods in Group Theory Book in PDF, ePub and Kindle
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.
| Author | : Ken Brown |
| Publisher | : Birkhäuser |
| Total Pages | : 339 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 303488205X |
Download Lectures on Algebraic Quantum Groups Book in PDF, ePub and Kindle
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
| Author | : Douglas C. Ravenel |
| Publisher | : American Mathematical Society |
| Total Pages | : 417 |
| Release | : 2023-02-09 |
| Genre | : Mathematics |
| ISBN | : 1470472937 |
Download Complex Cobordism and Stable Homotopy Groups of Spheres Book in PDF, ePub and Kindle
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 | : Paul Gregory Goerss |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 520 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821832859 |
Download Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory Book in PDF, ePub and Kindle
As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.
