Izmestiev, Ivan Klee, Steven Novik, Isabella 2017-11-07 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. application/pdf https://folia.unifr.ch/global/documents/306202 https://folia.unifr.ch/documents/306202/files/izm_smb.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2017.08.036 info:eu-repo/semantics/openAccess License undefined Advances in Mathematics. - 2017, vol. 320, no. Supplement C, p. 82–114 info:eu-repo/classification/udc/51 Simplicial moves on balanced complexes http://purl.org/coar/resource_type/c_6501