Simplicial shellable spheres via combinatorial blowups

Čukić, Sonja; Delucchi, Emanuele

doi:10.1090/S0002-9939-07-08768-0

Simplicial shellable spheres via combinatorial blowups
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by Sonja Lj. Čukić and Emanuele Delucchi

Proc. Amer. Math. Soc. 135 (2007), 2403-2414

DOI: https://doi.org/10.1090/S0002-9939-07-08768-0

Published electronically: April 10, 2007

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Abstract:

The construction of the Bier sphere $\textrm {Bier}(K)$ for a simplicial complex $K$ is due to Bier (1992). Björner, Paffenholz, Sjöstrand and Ziegler (2005) generalize this construction to obtain a Bier poset $\textrm {Bier}(P,I)$ from any bounded poset $P$ and any proper ideal $I\subseteq P$. They show shellability of $\textrm {Bier}(P,I)$ for the case $P=B_n$, the 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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