Simplicial shellable spheres via combinatorial blowups

Authors:
Sonja Lj. Cukic and Emanuele Delucchi

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

MSC (2000):
Primary 06A07, 55U10, 52B22

Published electronically:
April 10, 2007

MathSciNet review:
2302561

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Abstract | References | Similar Articles | Additional Information

Abstract: The construction of the Bier sphere for a simplicial complex is due to Bier (1992). Björner, Paffenholz, Sjöstrand and Ziegler (2005) generalize this construction to obtain a Bier poset from any bounded poset and any proper ideal . They show shellability of for the case , 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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Additional Information

**Sonja Lj. Cukic**

Affiliation:
Institute of Theoretical Computer Science, ETH Zurich, 8092 Zurich, Switzerland

Email:
sonja@math.binghamton.edu

**Emanuele Delucchi**

Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

Email:
delucchi@mail.dm.unipi.it

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

Keywords:
Posets,
lattices,
shellability,
combinatorial blowups,
building sets,
nested sets,
simplicial shellable spheres,
Bier posets,
Bier lattices

Received by editor(s):
February 2, 2006

Received by editor(s) in revised form:
May 2, 2006

Published electronically:
April 10, 2007

Additional Notes:
Research partially supported by TH-Projekt 0-20268-05, and by the Swiss National Science Foundation, project PP002–106403/1

Communicated by:
Paul Goerss

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.