BOUNDED COHOMOLOGY AND l1-HOMOLOGY OF THREE-MANIFOLDS
نویسنده
چکیده
In this paper we define, for each aspherical orientable 3-manifold M endowed with a torus splitting T , a 2-dimensional fundamental l1-class [M ] whose l1norm has similar properties as the Gromov simplicial volume of M (additivity under torus splittings and isometry under finite covering maps). Next, we use the Gromov simplicial volume of M and the l1-norm of [M ] to give a complete characterization of those nonzero degree maps f : M → N which are homotopic to a deg(f)-covering map. As an application we characterize those degree one maps f : M → N which are homotopic to a homeomorphism in terms of bounded cohomology classes.
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