Cohomology operators defined by a deformation
By viewing \(R\)-modules as differential graded modules over the Koszul complex resolving \(R\) over \(\mathbb{Q}\), the authors construct cohomology operators \(\chi_j:\text{Ext}^i_R(M,N)\to\text{Ext}^{i+1}_R(M,N)\) and \(\text{Tor}_i^K(L,M)\to\text{Tor}^K_{i-2}(L,M)\) and establish their main properties directly for complexes of \(R\)-modules. They give two different approaches, first à la Gulliksen, as connecting homomorphisms, second from chain-level maps, as did Eisenbud. The authors give direct proofs of their formal properties and in particular of their centrality. They compare the operators \(\chi_j\) to the cohomology operators previously constructed by Gulliksen, Eisenbud, Mehta and Avramov.
scientific article; zbMATH DE number 1218680