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arXiv · 1804.06270

Balanced shellings and moves on balanced manifolds

Martina Juhnke-Kubitzke·Lorenzo Venturello
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Abstract

A classical result by Pachner states that two $d$-dimensional combinatorial manifolds with boundary are PL homeomorphic if and only 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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Martina Juhnke-Kubitzke, Lorenzo Venturello. 2018-04-17. Balanced shellings and moves on balanced manifolds. https://arxiv.org/abs/1804.06270

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