Pure Postgrad Seminar - Dr M Pirashvili Seminar

Event details

We investigate the relationship between symmetric, exterior and the classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We show that there is a map from exterior cohomology to symmetric cohomology which is a split monomorphism in general and an isomorphism in many cases, but not always. A spectral sequence is constructed, which relates symmetric and classical cohomology groups. As a sample application we obtain that symmetric and classical cohomologies are isomorphic for torsion free groups.