Topological Frobenius algebras
Symplectic Geometry
2024-09-11 v2 Algebraic Topology
Rings and Algebras
Abstract
We define the notions of unital/counital/biunital infinitesimal anti-symmetric bialgebras and coFrobenius bialgebras and discuss their algebraic properties. We also define the notion of a graded 2D open-closed TQFT. These structures arise in Rabinowitz Floer homology, loop space homology, quantum homology, and the homology of finite dimensional manifolds. The underlying vector spaces, which are typically infinite dimensional, belong to a class of topological vector spaces known as Tate vector spaces.
Cite
@article{arxiv.2209.02979,
title = {Topological Frobenius algebras},
author = {Kai Cieliebak and Alexandru Oancea},
journal= {arXiv preprint arXiv:2209.02979},
year = {2024}
}
Comments
64 pages, 9 figures. v2: major revision, in which we use in a systematic way the formalism of Tate vector spaces. Title changed