6533b7d6fe1ef96bd12672ad

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Homeomorphic graph manifolds: A contribution to the μ constant problem

Peter B. ShalenB. Perron

subject

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-manifoldHomeomorphismMathematics

description

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.

yearjournalcountryeditionlanguage
1999-11-01Topology and its Applications
https://doi.org/10.1016/s0166-8641(98)00079-0