Stein domains and branched shadows of 4-manifolds |
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Authors: | Francesco Costantino |
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Institution: | (1) Institut de Recherche Mathématique Avancée, 7 Rue René Descartes, 67084 Strasbourg Cedex, France |
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Abstract: | We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact four-dimensional
Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit Stein, compact
neighborhoods. We base our calculations on Turaev’s shadows suitably “smoothed”; the conditions we find are purely algebraic
and combinatorial. Applying our results, we provide examples of hyperbolic 3-manifolds admitting “many” positive and negative
Stein fillable contact structures, and prove a four-dimensional analog of Oertel’s result on incompressibility of surfaces
carried by branched polyhedra.
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Keywords: | Stein domain Polyhedra Manifold Shadow |
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