Search results for "Graph manifold"

showing 2 items of 2 documents

Homeomorphic graph manifolds: A contribution to the μ constant problem

1999

Abstract We give a characterization, in terms of homological data in covering spaces, of those maps between (3-dimensional) graph manifolds which are homotopic to homeomorphisms. As an application we give a condition on a cobordism between graph manifolds that guarantees that they are homeomorphic. This in turn is applied to give a partial result on the μ -constant problem in (complex) dimension three.

SingularityDimension (graph theory)CobordismBanach manifoldHomology equivalenceCovering spaceμ constant problemMathematics::Algebraic TopologyMathematics::Geometric TopologyDistance-regular graphManifoldCombinatoricsCoxeter graphSeifert fibered spaceMilnor fiberGraph manifoldEdge-transitive graphRicci-flat manifoldComplex algebraic surfaceGeometry and TopologyMathematics::Symplectic Geometry3-manifoldHomeomorphismMathematicsTopology and its Applications
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Volume-convergent sequences of Haken 3-manifolds

2003

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).

Topological manifoldSequenceDegree (graph theory)Zero (complex analysis)General MedicineHaken manifoldMathematics::Geometric TopologyHomeomorphismCombinatoricsGraph manifoldMathematics::Differential GeometryMathematics::Symplectic GeometryMathematicsVolume (compression)Comptes Rendus Mathematique
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