TY - JOUR
T1 - Barycentric Subdivisions of Convex Complexes are Collapsible
AU - Adiprasito, Karim
AU - Benedetti, Bruno
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85075358744&partnerID=8YFLogxK
U2 - 10.1007/s00454-019-00137-3
DO - 10.1007/s00454-019-00137-3
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AN - SCOPUS:85075358744
SN - 0179-5376
VL - 64
SP - 608
EP - 626
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 3
ER -