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Local rigidity of aspherical three-manifolds

Pierre Derbez (2012)

Annales de l’institut Fourier

In this paper we construct, for each aspherical oriented 3 -manifold M , a 2 -dimensional class in the l 1 -homology of M whose norm combined with the Gromov simplicial volume of M gives a characterization of those nonzero degree maps from M to N which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of M and N .

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

We determine in n the form of curves C corresponding to strictly monotone functions as well as the components of affine connections for which any image of C under a compact-free group Ω of affinities containing the translation group is a geodesic with respect to . Special attention is paid to the case that Ω contains many dilatations or that C is a curve in 3 . If C is a curve in 3 and Ω is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

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