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.

Balanced triangulations on few vertices and an implementation of cross-fips

Venturello L.
2019

Abstract

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.
Venturello, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1153299
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