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Morse index of a cyclic polygon

Gaiane Panina, Alena Zhukova (2011)

Open Mathematics

It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.

Multifibrations. A class of shape fibrations with the path lifting property

Antonio Giraldo, José M. R. Sanjurjo (2001)

Czechoslovak Mathematical Journal

In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration. Multifibrations have the interesting property of being characterized in a completely intrinsic way by a path lifting property involving only the total and the base space of the fibration. We also show that multifibrations (and also, with some restrictions,...

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