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Hyperbolische Transformation konvexer Polyeder

Ralf Gollmer (1981)

Aplikace matematiky

Der Artikel beschäftigt sich mit einigen Eigenschaften von hyperbolischen, d. h. gebrochen-affinen, Transformationen, welche für die Bilder konvexer Polyeder bei solchen Transformationen von Bedeutung sind. Es wird eine explizite Darstellung des Bildes eines konvexen Polyeders durch Ecken und Kanten des Urbildpolyeders gewonnen, die Konvexität des Bildes und das Bild des relativen Inneren einer konvexen Menge untersucht.

Hyperideal polyhedra in hyperbolic 3-space

Xiliang Bao, Francis Bonahon (2002)

Bulletin de la Société Mathématique de France

A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic 3 -space 3 which, in the projective model for 3 ℝℙ 3 , is just the intersection of 3 with a projective polyhedron whose vertices are all outside 3 and whose edges all meet 3 . We classify hyperideal polyhedra, up to isometries of 3 , in terms of their combinatorial type and of their dihedral angles.

Hyperplane arrangements and Milnor fibrations

Alexander I. Suciu (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.

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