Higher structures on homology groups

Niels Kowalzig; Francesca Pratali

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arXiv · 2406.06710

Higher structures on homology groups

Niels Kowalzig·Francesca Pratali

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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 coantisymmetric 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.

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BibTeX RIS

Niels Kowalzig, Francesca Pratali. 2024-06-10. Higher structures on homology groups. https://arxiv.org/abs/2406.06710

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