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Mathematische Zeitschrift

, Volume 235, Issue 1, pp 159–171 | Cite as

Decompositions of simplicial balls and spheres with knots consisting of few edges

  • Masahiro Hachimori
  • Günter M. Ziegler
Original article

Abstract.

Constructibility is a condition on pure simplicial complexes that is weaker than shellability. In this paper we show that non-constructible triangulations of the d-dimensional sphere exist for every \(d \geq 3\). This answers a question of Danaraj and Klee [10]; it also strengthens a result of Lickorish [16] about non-shellable spheres. Furthermore, we provide a hierarchy of combinatorial decomposition properties that follow from the existence of a non-trivial knot with “few edges” in a 3-sphere or 3-ball, and a similar hierarchy for 3-balls with a knotted spanning arc that consists of “few edges.”

Keywords

Simplicial Complex Decomposition Property Simplicial Ball Similar Hierarchy Combinatorial Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Masahiro Hachimori
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Dept. Systems Science, University of Tokyo, 3–8–1, Komaba, Meguro, Tokyo 153-8902, Japan (e-mail: hachi@klee.c.u-tokyo.ac.jp)JP
  2. 2.Dept. Mathematics, MA 7–1, TU Berlin, 10623 Berlin, Germany (e-mail: ziegler@math.tu-berlin.de)DE

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