Alexander duality in subdivisions of Lawrence polytopes

Lawrence 多胞体的稳定性条件与细分

Stability conditions and subdivisions of Lawrence polytopes

本文研究图上的稳定性条件与退化集，证明退化集对应图拟阵的单元素扩张，并从 Lawrence 多胞体细分构造稳定性条件，建立与可定向扩张的联系。

Alexander猜想在无限单纯复形上的推广

Alexander's conjecture for infinite simplicial complexes

将Alexander猜想从有限单纯复形推广到无限单纯复形，证明任意两个具有共同子划分的无限三角剖分必有共同星形子划分。

所有三角剖分都有一个共同的星形细分

All triangulations have a common stellar subdivision

本文解决了PL拓扑与双有理几何中的两个长期未决问题：证明了Oda强因子分解猜想的加权版本及双有理环面簇的共同迭代爆破，并证明了Alexander于1930年提出的关于PL同胚多面体具有共同星形细分的猜想。

Stellar theory for flag complexes

Refining a basic result of Alexander, we show that two flag simplicial complexes are piecewise linearly homeomorphic if and only if they can be connected by a sequence of flag complexes, each obtained from the previous one by either an edge subdivision or its inverse. For flag spheres we pose new conjectures on their combinatorial structure forced by their face numbers, analogous to the extremal examples in the upper and lower bound theorems for simplicial spheres. Furthermore, we show that our algorithm to test the conjectures searches through the entire space of flag PL spheres of any given …