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Peter Zvengrowski - Diagonal formulae in group cohomology
PETER ZVENGROWSKI, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada | |
Diagonal formulae in group cohomology |
For any group G, its cohomology can be defined to be the cohomology of the Eilenberg-MacLane space K(G,1). From this definition, or otherwise, one sees that the cohomology with coefficients in a ring R forms a graded algebra under the cup product operation. One method to find these cup products is to start with a projective resolution of Z over the group ring ZG and then find a diagonal map . We will concern ourselves with the existence of explicit diagonal formulae of this type for certain groups arising as the fundamental group of a 3-manifold, with emphasis on the Seifert manifolds, and also mention some of the applications of the cup products.
eo@camel.math.ca