Subdivisions, Shellability, and collapsibility of products. (English) Zbl 1399.52025
Summary: We prove that the second derived subdivision of any rectilinear triangulation of any convex polytope is shellable. Also, we prove that the first derived subdivision of every rectilinear triangulation of any convex 3-dimensional polytope is shellable. This complements Mary Ellen Rudin’s classical example of a non-shellable rectilinear triangulation of the tetrahedron. Our main tool is a new relative notion of shellability that characterizes the behavior of shellable complexes under gluing.
MSC:
| 52B22 | Shellability for polytopes and polyhedra |
| 05E45 | Combinatorial aspects of simplicial complexes |
| 57Q10 | Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. |
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