Simplicial shellable spheres via combinatorial blowups

Čukić, Sonja Lj. and Delucchi, Emanuele (2007) Simplicial shellable spheres via combinatorial blowups. Proceedings of the American Mathematical Society, 135 (08). pp. 2403-2415. ISSN 0002-9939

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The construction of the Bier sphere Bier(K for a simplicial complex K is due to Bier (1992). Björner, Paffenholz, Sjöstrand and Ziegler (2005) generalize this construction to obtain a Bier poset Bier(P,I) from any bounded poset P and any proper ideal I in P. They show shellability of Bier(P,I) for the case when P is a finite boolean lattice, and thereby obtain ‘many shellable spheres’ in the sense of Kalai (1988). We put the Bier construction into the general framework of the theory of nested set complexes of Feichtner and Kozlov (2004). We obtain ‘more shellable spheres’ by proving the general statement that combinatorial blowups, hence stellar subdivisions, preserve shellability.

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