Advanced Course on Classifiying Spaces and Cohomology of Groups
Sign into June 02, 1998
Coordinator
C. Broto (UAB)
SPEAKERS
W. G. Dwyer (University of Notre Dame)
Title: Finite groups, homotopy colimits, and homology decompositions
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We use homotopy theory to study the problem of calculating the cohomology of the classifying space of a finite group. The approach is to express the classifying space, up to cohomology, as a homotopy colimit of classifying spaces of smaller groups. Doing this in a systematic way involves working with simplicial techniques, studying homotopy colimits, and analyzing the fixed-point set geometry of a space with an action of a finite group. |
H.-W. Henn (Université Louis Pasteur, Strasbourg)
Title: Unstable modules over the Steenrod algebra and cohomology of groups
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The presence of Steenrod operations in the mod – p cohomology ring H*(BG, Fp) of the classifying space BG of a group G allows to understand qualitative features of this ring, at least for a large class of groups including all compact Lie groups but also for many discrete groups like arithmetic groups, mapping class groups and automorphism groups of free groups. The relevant theory of unstable modules over the Steenrod algebra was explained and the way the general theory can be applied to do concrete calculations was shown. |
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