On the Cohomology Ring of an Algebra
  We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum multiplication on Floer cohomology of free loop spaces. We discuss some examples, as well as applications to index theorems, characteristic classes and deformations. 
Pyszard Nest (University of Copenhagen), Boris Tsygan (Penn State   University)