6533b82ffe1ef96bd129478a

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A criterion for homeomorphism between closed Haken manifolds

Pierre Derbez

subject

Pure mathematicsHaken manifoldHaken manifoldAlgebraic topologyGromov simplicial volumeMathematics::Algebraic TopologyCombinatoricsMathematics - Geometric TopologySeifert fibered spaceSimple (abstract algebra)FOS: Mathematicsfinite coveringMathematics::Symplectic Geometry57M50 51H20MathematicsHomotopyhyperbolic manifoldhomology equivalenceGeometric Topology (math.GT)General MedicineMathematics::Geometric Topology57M50ManifoldHomeomorphism51H20Geometry and Topology

description

In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.

yearjournalcountryeditionlanguage
2003-04-05Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
https://doi.org/10.1016/s0764-4442(00)01742-0