Bounded Cohomology and $l_1$-Homology of Three-Manifolds

dc.creatorDerbez, P.
dc.date2008-09-25
dc.date.accessioned2026-07-07T10:05:20Z
dc.date.available2026-07-07T10:05:20Z
dc.descriptionIn this paper we define, for each aspherical orientable 3-manifold $M$ endowed with a \emph{torus splitting} $Ţ$, a 2-dimensional fundamental $l_1$-class $[M]^{Ţ}$ whose $l_1$-norm 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 $l_1$-norm of $[M]^{Ţ}$ to give a complete characterization of those nonzero degree maps $f\co M\to N$ which are homotopic to a ${\rm deg}(f)$-covering map. As an application we characterize those degree one maps $f\co M\to N$ which are homotopic to a homeomorphism in terms of bounded cohomology classes.
dc.identifierhttps://arxiv.org/abs/0809.4446
dc.identifierhttp://arxiv.org/abs/0809.4446
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169980
dc.subjectGeometric Topology
dc.subject57M50, 51H20
dc.titleBounded Cohomology and $l_1$-Homology of Three-Manifolds
dc.typetext

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