Barycentric Subdivisions of Convex Complexes are Collapsible
Barycentric Subdivisions of Convex Complexes are Collapsible
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DOI：
10.1007/s00454-019-00137-3
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发表时间：
2017-09
影响因子：
0.8
通讯作者：
Karim A. Adiprasito;Bruno Benedetti
中科院分区：
文献类型：
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作者：
Karim A. Adiprasito;Bruno Benedetti
PL拓扑中的一个经典问题，由Hudson， Lickorish和Kirby等人提出，是单纯形的每个线性细分是否都是可简单折叠的。已知答案是正的。通过证明任何多面体的任何线性细分在最多一个质心细分后是可简单折叠的，我们解决了这个问题直至一个细分。进一步证明了任何星形多面体的任何线性细分最多是简单可折叠后导细分。这在古德里克提出的一个老问题上取得了进展。
A classical question in PL topology, asked among others by Hudson, Lickorish, and Kirby, is whether every linear subdivision of thed-simplex is simplicially collapsible. The answer is known to be positive for. 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 inis simplicially collapsible afterderived subdivisions at most. This presents progress on an old question by Goodrick.