Simplicial moves on balanced complexes

Izmestiev, Ivan; Klee, Steven; Novik, Isabella

doi:10.1016/j.aim.2017.08.036

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Journal article

Simplicial moves on balanced complexes

Izmestiev, Ivan University of Fribourg Department of Mathematics, Fribourg, Switzerland
Klee, Steven Seattle University Department of Mathematics, Seattle, USA
Novik, Isabella University of Washington Department of Mathematics, Seattle, USA

07.11.2017

Published in:

Advances in Mathematics. - 2017, vol. 320, no. Supplement C, p. 82–114

English We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly (d+1)-colored) triangulation of a combinatorial d-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also known as Pachner moves). Specifically, we establish the following theorem: any two balanced triangulations of a closed combinatorial d-manifold can be connected by a sequence of cross-flips. Along the way we prove that for every m≥d+2 and any closed combinatorial d-manifold M, two m-colored triangulations of M can be connected by a sequence of bistellar flips that preserve the vertex colorings.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language