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Juhnke-Kubitzke, Martina; Venturello, Lorenzo
Advances in mathematics (New York. 1965), 03/2021, Volume: 379Journal Article
A classical result by Pachner states that two d-dimensional combinatorial manifolds with boundary are PL homeomorphic if and only if they can be connected by a sequence of shellings and inverse shellings. We prove that for balanced, i.e., properly (d+1)-colored, manifolds such a sequence can be chosen such that balancedness is preserved in each step. As a key ingredient we establish that any two balanced PL homeomorphic combinatorial manifolds with the same boundary are connected by a sequence of basic cross-flips, as was shown recently by Izmestiev, Klee and Novik for balanced manifolds without boundary. Moreover, we enumerate combinatorially different basic cross-flips and show that roughly half of these suffice to relate any two PL homeomorphic manifolds.
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