From Representation Theory To Homotopy Groups
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| Author | : Donald M. Davis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 65 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829874 |
A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applys this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989.
| Author | : T. Tom Dieck |
| Publisher | : Springer |
| Total Pages | : 317 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540385177 |
| Author | : Hans-Joachim Baues |
| Publisher | : |
| Total Pages | : 17 |
| Release | : 1998 |
| Genre | : |
| ISBN | : |
| Author | : Mark E. Mahowald |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821808052 |
The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
| Author | : Tammo tom Dieck |
| Publisher | : Walter de Gruyter |
| Total Pages | : 325 |
| Release | : 2011-04-20 |
| Genre | : Mathematics |
| ISBN | : 3110858371 |
“This book is a jewel – it explains important, useful and deep topics in Algebraic Topology that you won’t find elsewhere, carefully and in detail.” Prof. Günter M. Ziegler, TU Berlin
| Author | : Luchezar L. Avramov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 352 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821838148 |
This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.
| Author | : Jon F. Carlson |
| Publisher | : Springer |
| Total Pages | : 493 |
| Release | : 2018-10-04 |
| Genre | : Mathematics |
| ISBN | : 3319940333 |
These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
| Author | : William G. Dwyer |
| Publisher | : Birkhäuser |
| Total Pages | : 106 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883560 |
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 | : K Heiner Kamps |
| Publisher | : World Scientific |
| Total Pages | : 476 |
| Release | : 1997-04-11 |
| Genre | : Mathematics |
| ISBN | : 9814502553 |
The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).
| Author | : J. Peter May |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 384 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821803190 |
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
