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
Journal: ELECTRONIC JOURNAL OF COMBINATORICS
Volumen: 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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