Constructing Combinatorial 4-Manifolds

Details Constructing Combinatorial 4-Manifolds Constructing Combinatorial 4-Manifolds

2007-07-10

arxiv.org/abs/0707.1415v1

Mathematics

Combinatorics

Stronger results and a shorter proof are presented in "Constructing Simplicial Branched Covers" by the author. Nevertheless we

Scientific paper

Every closed oriented PL 4-manifold is a branched cover of the 4-sphere branched over a PL-surface with finitely many singularities by Piergallini [Topology 34(3):497-508, 1995]. This generalizes a long standing result by Hilden and Montesinos to dimension four. Izmestiev and Joswig [Adv. Geom. 3(2):191-225, 2003] gave a combinatorial equivalent of the Hilden and Montesinos result, constructing closed oriented combinatorial 3-manifolds as simplicial branched covers of combinatorial 3-spheres. The construction of Izmestiev and Joswig is generalized and applied to the result of Piergallini, obtaining closed oriented combinatorial 4-manifolds as simplicial branched covers of simplicial 4-spheres.

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