Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- Part 1 Multiplication on the tangent bundle -- Chapter 1 Introduction to part 1 -- 1.1 First examples -- 1.2 Fast track through the results -- Chapter 2 Definition and first properties of F-manifolds -- 2.1 Finite-dimensional algebras -- 2.2 Vector bundles with multiplication -- 2.3 Definition of F-manifolds -- 2.4 Decomposition of F-manifolds and examples -- 2.5 F-manifolds and potentiality -- Chapter 3 Massive F-manifolds and Lagrange maps -- 3.1 Lagrange property of massive F-manifolds -- 3.2 Existence of Euler fields -- 3.3 Lyashko-Looijenga maps and graphs of Lagrange maps -- 3.4 Miniversal Lagrange maps and F-manifolds -- 3.5 Lyashko-Looijenga map of an F-manifold -- Chapter 4 Discriminants and modality of F-manifolds -- 4.1 Discriminant of an F-manifold -- 4.2 2-dimensional F-manifolds -- 4.3 Logarithmic vector fields -- 4.4 Isomorphisms and modality of germs of F-manifolds -- 4.5 Analytic spectrum embedded differently -- Chapter 5 Singularities and Coxeter groups -- 5.1 Hypersurface singularities -- 5.2 Boundary singularities -- 5.3 Coxeter groups and F-manifolds -- 5.4 Coxeter groups and Frobenius manifolds -- 5.5 3-dimensional and other F-manifolds -- Part 2 Frobenius manifolds, Gauß-Manin connections, and moduli spaces for hypersurface singularities -- Chapter 6 Introduction to part 2 -- 6.1 Construction of Frobenius manifolds for singularities -- 6.2 Moduli spaces and other applications -- Chapter 7 Connections over the punctured plane -- 7.1 Flat vector bundles on the punctured plane -- 7.2 Lattices -- 7.3 Saturated lattices -- 7.4 Riemann-Hilbert-Birkhoff problem -- 7.5 Spectral numbers globally -- Chapter 8 Meromorphic connections -- 8.1 Logarithmic vector fields and differential forms -- 8.2 Logarithmic pole along a smooth divisor.

8.3 Logarithmic pole along any divisor -- 8.4 Remarks on regular singular connections -- Chapter 9 Frobenius manifolds and second structure connections -- 9.1 Definition of Frobenius manifolds -- 9.2 Second structure connections -- 9.3 First structure connections -- 9.4 From the strcuture connections to metric and multiplication -- 9.5 Massive Frobenius manifolds -- Chapter 10 Gauß-Manin connections for hypersurface singularities -- 10.1 Semiuniversal unfoldings and F-manifolds -- 10.2 Cohomology bundle -- 10.3 Gauß-Manin connection -- 10.4 Higher residue pairings -- 10.5 Polarized mixed Hodge structures and opposite filtrations -- 10.6 Brieskorn lattice -- Chapter 11 Frobenius manifolds for hypersurface singularities -- 11.1 Construction of Frobenius manifolds -- 11.2 Deformed flat coordinates -- 11.3 Remarks on mirror symmetry -- 11.4 Remarks on oscillating integrals -- Chapter 12 u-constant stratum -- 12.1 Canonical complex structure -- 12.2 Period map and infinitesimal Torelli -- Chapter 13 Moduli spaces for singularities -- 13.1 Compatibilities -- 13.2 Symmetries of singularities -- 13.3 Global moduli spaces for singularities -- Chapter 14 Variance of the spectral numbers -- 14.1 Socle field -- 14.2 G-function of a massive Frobenius manifold -- 14.3 Variance of the spectrum -- Bibliography -- Index.