Balanced shellings and moves on balanced manifolds

Autor(en): Juhnke-Kubitzke, Martina 
Venturello, Lorenzo
Stichwörter: Balancedness; Combinatorial manifold; Cross-flips; DECOMPOSITIONS; Mathematics; Shellability; SHELLABLE NONPURE COMPLEXES; Simplicial complex; SPHERES; TRIANGULATIONS
Erscheinungsdatum: 2021
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN MATHEMATICS
Volumen: 379
Zusammenfassung: 
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. (C) 2021 Elsevier Inc. All rights reserved.
ISSN: 00018708
DOI: 10.1016/j.aim.2021.107571

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