On adding a variable to a Frobenius manifold and generalizations

@article{David2012OnAA,
  title={On adding a variable to a Frobenius manifold and generalizations},
  author={Liana David},
  journal={Geometriae Dedicata},
  year={2012},
  volume={167},
  pages={189-214}
}
  • L. David
  • Published 4 January 2012
  • Mathematics
  • Geometriae Dedicata
Let $$\pi :V\rightarrow M$$ be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure $$(\circ _{M},e_{M},g_{M})$$ and typical fiber has the structure of a Frobenius algebra $$(\circ _{V},e_{V},g_{V})$$. Using a connection $$D$$ on the bundle $$\pi : V{\,\rightarrow \,}M$$ and a morphism $$\alpha :V\rightarrow TM$$, we construct an almost Frobenius structure $$(\circ , e_{V},g)$$ on the manifold $$V$$ and we study when it is Frobenius. In particular, we describe all… 

References

SHOWING 1-10 OF 19 REFERENCES

Weak Frobenius manifolds

We establish a new universal relation between the Lie bracket and $\circ$-multiplication of tangent fields on any Frobenius (super)manifold. We use this identity in order to introduce the notion of

tt* geometry, Frobenius manifolds, their connections, and the construction for singularities

The base space of a semiuniversal unfolding of a hypersurface singularity carries a rich geometry. By work of K. Saito and M. Saito is can be equipped with the structure of a Frobenius manifold. By

On the structure of Brieskorn lattices, II

We give a simple proof of the uniqueness of extensions of good sections for formal Brieskorn lattices, which can be used in a paper of C. Li, S. Li, and K. Saito for the proof of convergence in the

On the structure of Brieskorn lattice

the filtration F on Ox' The right hand side of (*) was first studied J f by Brieskorn [B] and we call it the Brieskorn lattice of M, and denote it by Mo. In fact, he defined the regular singular

Period Mapping Associated to a Primitive Form

The aim of this note is to give a summary of the study of primitive forms and period mappings associated with a universal unfolding F of an isolated hypersurface singularity, which was studied in

Frobenius Manifolds and Moduli Spaces for Singularities

Part I. Multiplication on the Tangent Bundle: 1. Introduction to part 1 2. Definition and first properties of F-manifolds 3. Massive F-manifolds and Lagrange maps 4. Discriminants and modality of

Isomonodromic Deformations and Frobenius Manifolds: An Introduction

The language of fibre bundles.- Holomorphic vector bundles on the Riemann sphere.- The Riemann-Hilbert correspondence on a Riemann surface.- Lattices.- The Riemann-Hilbert problem and Birkhoff's

Frobenius manifolds, quantum cohomology, and moduli spaces

Introduction: What is quantum cohomology? Introduction to Frobenius manifolds Frobenius manifolds and isomonodromic deformations Frobenius manifolds and moduli spaces of curves Operads, graphs, and