Homotopy Theoretic Methods in Group Cohomology

Dwyer, William G.; Henn, Hans-Werner

ISBN 10: 3764366052 / ISBN 13: 9783764366056

Editore: Birkhauser Verlag AG, 2001

Looks at group cohomology with tools that come from homotopy theory that give both decomposition theorems (which rely on homotopy colimits to obtain a description of the cohomology of a group in terms of the cohomology of suitable subgroups) and global structure theorems (which exploit the action of the ring of topological cohomology operations). Series: Advanced Courses in Mathematics - CRM Barcelona. Num Pages: 107 pages, 4 black & white illustrations, biography. BIC Classification: PBG; PBPD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 244 x 170 x 5. Weight in Grams: 193. . 2001. Paperback. . . . . Books ship from the US and Ireland. Codice articolo V9783764366056

Riassunto:

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.

Contenuti: Classifying Spaces and Homology Decompositions.- Cohomology of Groups and Unstable Modules over the Steenrod Algebra.

Dati bibliografici

Titolo: Homotopy Theoretic Methods in Group ...
Casa editrice: Birkhauser Verlag AG
Data di pubblicazione: 2001
Legatura: Brossura
Condizione: New