High Quality Content by WIKIPEDIA articles! In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a family of algebraic varieties. The base space is taken to be the set of parameters defining the family, and the fibres are taken to be the de Rham cohomology group of the variety V. Flat sections of the bundle are described by differential equations; the best-known of these is the Picard-Fuchs equation, which arises when the family of varieties is taken to be the family of elliptic curves. In intuitive terms, when the family is locally trivial, cohomology classes can be moved from one fibre in the family to nearby fibres, providing the 'flat section' concept in purely topological terms. The existence of the connection is to be inferred from the flat sections.

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