Gauss-Manin connections of Schläfli type for hypersphere arrangements
[Connexions de Gauss-Manin de type Schläfli pour des arrangements hypersphériques]
Aomoto, Kazuhiko1
1 University of Nagoya, Department of Mathematics, Nagoya (Japon)
Annales de l'Institut Fourier, Colloque en l'honneur de Frédéric Pham, Tome 53 (2003) no. 4, pp. 977-995.

Nous donnons la structure cohomologique des arrangements hypersphériques. Les connexions de Gauss-Manin pour les intégrales hypergéométriques associées sont données en termes de formes invariantes. Elles sont utilisées pour obtenir la formule explicite du volume d'un simplexe dont les faces sont hypersphériques.

The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.

DOI : 10.5802/aif.1970
Classification : 32S22, 32S40, 33C70, 39B32
Keywords: hypersphere arrangements, twisted cohomology, Gauss-Manin connection
Mot clés : arrangements hypersphériques, cohomologie des n{\oe}uds, connexion de Gauss-Manin
Aomoto, Kazuhiko 1

1 University of Nagoya, Department of Mathematics, Nagoya (Japon) 
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Aomoto, Kazuhiko. Gauss-Manin connections of Schläfli type for hypersphere arrangements. Annales de l'Institut Fourier, Colloque en l'honneur de Frédéric Pham, Tome 53 (2003) no. 4, pp. 977-995. doi : 10.5802/aif.1970. http://www.numdam.org/articles/10.5802/aif.1970/

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