Bier Spheres and Posets

@article{Bjrner2005BierSA,
  title={Bier Spheres and Posets},
  author={A. Bj{\"o}rner and A. Paffenholz and Jonas Sj{\"o}strand and G. Ziegler},
  journal={Discrete & Computational Geometry},
  year={2005},
  volume={34},
  pages={71-86}
}
  • A. Björner, A. Paffenholz, +1 author G. Ziegler
  • Published 2005
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • Abstract In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n – 2)-spheres on 2n vertices, as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bier’s construction: the Bier posets Bier(P, I) of an arbitrary bounded poset P of… CONTINUE READING
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