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Homotopy Theoretic Methods in Group Cohomology (Advanced Courses in Mathematics - CRM Barcelona)
Rok: 2002
ISBN: 9783764366056
OKCZID: 110049020
Citace (dle ČSN ISO 690):
DWYER, William G. Homotopy theoretic methods in group cohomology. Basel: Birkhäuser Verlag, c2001. viii, 98 s. Advanced courses in mathematics, CRM Barcelona.
Anotace
This book looks at group cohomology with tools that come from homotopy theory. These tools 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). The approach is expository and thus suitable for graduate students and others who would like an introduction to the subject that organizes and adds to the relevant literature and leads to the frontier of current research. The book should also be interesting to anyone who wishes to learn some of the machinery of homotopy theory (simplicial sets, homotopy colimits, Lannes' T-functor, the theory of unstable modules over the Steenrod algebra) by seeing how it is used in a practical setting.