The low-dimensional homology of crossed modules.
For Γ a group of finite virtual cohomological dimension and a prime p, the p-period of Γ is defined to be the least positive integer d such that Farrell cohomology groups Hi(Γ; M) and Hi+d(Γ; M) have naturally isomorphic ZΓ modules M.We generalize a result of Swan on the p-period of a finite p-periodic group to a p-periodic infinite group, i.e., we prove that the p-period of a p-periodic group Γ of finite vcd is 2LCM(|N(〈x〉) / C(〈x〉)|) if the Γ has a finite quotient whose a p-Sylow subgroup is elementary...
Nous donnons une nouvelle construction cohomologique du cœur de l'invariant de Casson et nous donnons un nouveau calcul de ses valeurs sur les générateurs du sous- groupe de Johnson du mapping class group.