Barycentric Subdivisions of Convex Complexes are Collapsible

Karim Adiprasito, Bruno Benedetti

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A classical question in PL topology, asked among others by Hudson, Lickorish, and Kirby, is whether every linear subdivision of the d-simplex is simplicially collapsible. The answer is known to be positive for d≤ 3. We solve the problem up to one subdivision, by proving that any linear subdivision of any polytope is simplicially collapsible after at most one barycentric subdivision. Furthermore, we prove that any linear subdivision of any star-shaped polyhedron in Rd is simplicially collapsible after d- 2 derived subdivisions at most. This presents progress on an old question by Goodrick.

Original languageEnglish (US)
Pages (from-to)608-626
Number of pages19
JournalDiscrete and Computational Geometry
Issue number3
StatePublished - Oct 1 2020

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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