论文标题
子词复合体和卡莱（Kalai）关于重建球的猜想
Subword Complexes and Kalai's Conjecture on Reconstruction of Spheres
论文作者
论文摘要
多层理论中著名的定理指出，简单多层的组合类型完全由其刻度 - ridge图确定。 1987年，Blind and Mani通过使用同源性理论的拓扑工具进行了非构造性证明证明了这一著名的结果。 Kalai不久后给出了优雅的建设性证明。在他们的原始论文中，盲人和玛尼询问他们的结果是否可以扩展到简单的领域，而卡莱（Kalai）在2009年对他们的问题进行了积极的答案。在本文中，我们表明，在克纳特森（Knutson）和米勒（Miller）的球形子字体中，卡莱（Kalai）的猜想成立。这个简单球的家族是在Coxeter组的背景下出现的，并被认为是多面的。相比之下，并非所有流形都是可重建的。我们展示了两个明确的例子，即圆环和投射平面。
A famous theorem in polytope theory states that the combinatorial type of a simplicial polytope is completely determined by its facet-ridge graph. This celebrated result was proven by Blind and Mani in 1987, via a non-constructive proof using topological tools from homology theory. An elegant constructive proof was given by Kalai shortly after. In their original paper, Blind and Mani asked whether their result can be extended to simplicial spheres, and a positive answer to their question was conjectured by Kalai in 2009. In this paper, we show that Kalai's conjecture holds in the particular case of Knutson and Miller's spherical subword complexes. This family of simplicial spheres arises in the context of Coxeter groups, and is conjectured to be polytopal. In contrast, not all manifolds are reconstructible. We show two explicit examples, namely the torus and the projective plane.
