Nested set complexes for posets and the Bier construction

Lehmann, Juliane

doi:10.1090/S0002-9939-08-09503-8

Nested set complexes for posets and the Bier construction
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Proc. Amer. Math. Soc. 136 (2008), 3785-3793 Request permission

Abstract:

We generalize the concept of combinatorial nested set complexes to posets and exhibit the topological relationship between the arising nested set complexes and the order complex of the underlying poset. In particular, a sufficient condition is given so that this relationship is actually a subdivision.

We use the results to generalize the proof method of Čukić and Delucchi, so far restricted to semilattices, for a result of Björner, Paffenholz, Sjöstrand and Ziegler on the Bier construction on posets.

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