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Gauss-Manin connections of Schläfli type for hypersphere arrangements

Kazuhiko Aomoto (2003)

Annales de l’institut Fourier

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.

General construction of non-dense disjoint iteration groups on the circle

Krzysztof Ciepliński (2005)

Czechoslovak Mathematical Journal

Let = { F v 𝕊 1 𝕊 1 , v V } be a disjoint iteration group on the unit circle 𝕊 1 , that is a family of homeomorphisms such that F v 1 F v 2 = F v 1 + v 2 for v 1 , v 2 V and each F v either is the identity mapping or has no fixed point ( ( V , + ) is a 2 -divisible nontrivial Abelian group). Denote by L the set of all cluster points of { F v ( z ) , v V } for z 𝕊 1 . In this paper we give a general construction of disjoint iteration groups for which L 𝕊 1 .

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