Workshop, Niels Kowalzig: Higher structures on homology groups

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.