Balanced triangulations on few vertices and an implementation of cross-flips
Autor(en): | Venturello, Lorenzo | Stichwörter: | MANIFOLDS; Mathematics; Mathematics, Applied | Erscheinungsdatum: | 2019 | Herausgeber: | ELECTRONIC JOURNAL OF COMBINATORICS | Enthalten in: | ELECTRONIC JOURNAL OF COMBINATORICS | Band: | 26 | Ausgabe: | 3 | Zusammenfassung: | A d-dimensional simplicial complex is balanced if the underlying graph is (d 1)-colorable. We present an implementation of cross-flips, a set of local moves introduced by Izmestiev, Klee and Novik which connect any two PL-homeomorphic balanced combinatorial manifolds. As a result we exhibit a vertex minimal balanced triangulation of the real projective plane, of the dunce hat and of the real projective space, as well as several balanced triangulations of surfaces and 3-manifolds on few vertices. In particular we construct small balanced triangulations of the 3-sphere that are non-shellable and shellable but not vertex decomposable. |
ISSN: | 10778926 |
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