Speaker
Niels Kowalzig, University of Rome
Abstract
We dualise the classical fact that an operad with multiplication leads to cohomology
groups which form a Gerstenhaber algebra to the context of cooperads: as
a result, a cooperad with comultiplication induces a homology theory that is endowed with the
structure of a Gerstenhaber coalgebra, that is, it comes with a (graded cocommutative) coproduct
which is compatible with a cobracket in a dual Leibniz sense. As an application, one obtains
Gerstenhaber coalgebra structures on Tor groups over bialgebras or Hopf algebras, as
well as on Hochschild homology for Frobenius algebras. Joint work with Francesca Pratali.