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
Published in:
 Advances in Mathematics.  2017, vol. 320, no. Supplement C, p. 82–114
English
We introduce a notion of crossflips: local moves that transform a balanced (i.e., properly (d+1)colored) triangulation of a combinatorial dmanifold 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 dmanifold can be connected by a sequence of crossflips. Along the way we prove that for every m≥d+2 and any closed combinatorial dmanifold M, two mcolored 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

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Mathematics

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https://folia.unifr.ch/unifr/documents/306202
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