Local rigidity of aspherical three-manifolds
For each aspherical oriented \(3\)-manifold \(M\), the author constructs a \(2\)-dimensional class in the \(l_1\)-topology of \(M\) whose norm combined with the Gromov simplicial volume of \(M\) gives a characterisation of the non-zero degree maps from \(M\) to \(N\) which are homotopic to a covering map (here, \(N\) refers to some closed orientable irreducible \(3\)-manifold). It is then shown how to apply this result in order to characterise maps of degree \(1\) which are homotopic to a homeomorphism in terms of isometries between the bounded cohomology groups of \(M\) and \(N\).
scientific article; zbMATH DE number 6064521
scientific article