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RESEARCH PRODUCT
Volume-convergent sequences of Haken 3-manifolds
P. Derbezsubject
Topological manifoldSequenceDegree (graph theory)Zero (complex analysis)General MedicineHaken manifoldMathematics::Geometric TopologyHomeomorphismCombinatoricsGraph manifoldMathematics::Differential GeometryMathematics::Symplectic GeometryMathematicsVolume (compression)description
Abstract Let M be a closed orientable 3-manifold and let Vol(M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps f i :M→N i to Haken manifolds. We prove that any sequence of Haken manifolds (Ni,fi), satisfying limi→∞deg(fi)×Vol(Ni)=Vol(M) is finite up to homeomorphism. As an application, we deduce from this fact that any closed orientable 3-manifold with zero Gromov simplicial volume and in particular any graph manifold dominates at most finitely many Haken 3-manifolds. To cite this article: P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-05-01 | Comptes Rendus Mathematique |