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


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.”


Simplicial Complex Decomposition Property Simplicial Ball Similar Hierarchy Combinatorial Decomposition 
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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:
  2. 2.Dept. Mathematics, MA 7–1, TU Berlin, 10623 Berlin, Germany (e-mail:

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