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Topological Frobenius algebras

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arxiv 2209.02979 v2 pith:KJTRLDVT submitted 2022-09-07 math.SG math.ATmath.RA

Topological Frobenius algebras

Kai Cieliebak , Alexandru Oancea This is my paper
classification math.SG math.ATmath.RA
keywords homologyspacesvectorbialgebrasdefinedimensionaltopologicalalgebraic
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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.

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  1. Rabinowitz Floer homology for Legendrian submanifolds in prequantization bundles

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    Defines Rabinowitz Floer homology for Legendrian submanifolds in prequantization bundles and establishes an isomorphism to quantum homology of the underlying Lagrangian, enabling computations for spheres in quadrics a...