Simplicial shellable spheres via combinatorial blowups

Details Simplicial shellable spheres via combinatorial blowups Simplicial shellable spheres via combinatorial blowups

2006-02-06

arxiv.org/abs/math/0602101v1

Mathematics

Combinatorics

11 pages, 3 figures

Scientific paper

The construction of the Bier sphere Bier(K) for a simplicial complex K is due to Bier. Bj\"orner, Paffenholz, Sj\"ostrand and Ziegler generalize this construction to obtain a Bier poset Bier(P,I) from any bounded poset P and any proper ideal I of P. They show shellability of Bier(P,I) for the case where P is the boolean lattice, and obtain thereby 'many shellable spheres' in the sense of Kalai. We put the Bier construction into the general framework of the theory of nested set complexes of Feichtner and Kozlov. We obtain 'more shellable spheres' by proving the general statement that combinatorial blowups, hence stellar subdivisions, preserve shellability.

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