Homotopy Theoretic Methods in Group CohomologyThis 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. |
Other editions - View all
Homotopy Theoretic Methods in Group Cohomology William G. Dwyer,Hans-Werner Henn Limited preview - 2012 |
Homotopy Theoretic Methods in Group Cohomology William G Dwyer,Hans-Werner Henn No preview available - 2001 |
Common terms and phrases
abelian group abstract simplicial complex action of G acyclic Ap(G CG(E chain complex classifying space coefficient functors compact Lie group computation constant functor construction CW-complex denote diagram discrete group elementary abelian p-subgroups elements Example finite group Fp-algebra Fp-vector spaces functor F G-module G-sets G-space geometric realization group cohomology group G H*BCG(E H*BG H*BV HLS3 hocolim F homology decomposition homology spectral sequence homomorphism homotopy colimit Homu identity functor induces an isomorphism injective invariant isotropy spectral sequence Lannes group Lemma Leray spectral sequence Let G map f mod p homology mod-p cohomology morphisms n-simplex natural map natural transformations nerve nilpotent non-identity non-trivial ordered simplicial complex p-group prime profinite proof Proposition pushout Quillen groups Quillen's theorem resp result simplex simplicial object simplicial sets simplicial space small category Steenrod algebra subgroup of G Suppose trivial unstable algebras unstable modules weak equivalence weakly
References to this book
Cohomology Rings of Finite Groups: With an Appendix: Calculations of ... Jon Carlson Limited preview - 2003 |