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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Simplicial shellable spheres via combinatorial blowups
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by Sonja Lj. Čukić and Emanuele Delucchi PDF
Proc. Amer. Math. Soc. 135 (2007), 2403-2414 Request permission

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.
References
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Additional Information
  • Sonja Lj. Čukić
  • 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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2403-2414
  • MSC (2000): Primary 06A07, 55U10, 52B22
  • DOI: https://doi.org/10.1090/S0002-9939-07-08768-0
  • MathSciNet review: 2302561