Constructing Combinatorial 4-Manifolds
| dc.creator | Witte, Nikolaus | |
| dc.date | 2007-07-10 | |
| dc.date.accessioned | 2026-07-07T08:14:50Z | |
| dc.date.available | 2026-07-07T08:14:50Z | |
| dc.description | 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. | |
| dc.description | Stronger results and a shorter proof are presented in "Constructing Simplicial Branched Covers" by the author. Nevertheless we present some interesting techniques and a combinatorial analog of the (topological) proof by Piergallini | |
| dc.identifier | https://arxiv.org/abs/0707.1415 | |
| dc.identifier | http://arxiv.org/abs/0707.1415 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133274 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M12; 57Q99; 05C15; 57M25 | |
| dc.title | Constructing Combinatorial 4-Manifolds | |
| dc.type | text |