Graded Frobenius Algebras
Algebraic Topology
2025-08-05 v2 Quantum Algebra
Abstract
We construct a PROP which encodes 2D-TQFTs with a grading. This defines a graded Frobenius algebra as algebras over this PROP. We also give a description of graded Frobenius algebras in terms of maps and relations. This structure naturally arises as the cohomology of manifolds, loop homology and Hochschild homology of Frobenius algebras. In addition, we give a comprehensive description of the signs that arise in suspending algebras over PROPs.
Cite
@article{arxiv.2412.13909,
title = {Graded Frobenius Algebras},
author = {Jonathan Clivio},
journal= {arXiv preprint arXiv:2412.13909},
year = {2025}
}
Comments
This is the published version. Added the case of graded Frobenius algebras which are neither symmetric or commutative and other minor revisions