Bounded Cohomology and $l_1$-Homology of Three-Manifolds
| dc.creator | Derbez, P. | |
| dc.date | 2008-09-25 | |
| dc.date.accessioned | 2026-07-07T10:05:20Z | |
| dc.date.available | 2026-07-07T10:05:20Z | |
| dc.description | In 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.identifier | https://arxiv.org/abs/0809.4446 | |
| dc.identifier | http://arxiv.org/abs/0809.4446 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169980 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50, 51H20 | |
| dc.title | Bounded Cohomology and $l_1$-Homology of Three-Manifolds | |
| dc.type | text |