论文标题
产品上的莫尔斯炮击
Morse shellings on products
论文作者
论文摘要
我们最近定义了有限的简单复合物的莫尔斯毛发性（和润滑性）的特性，该络合物扩展了经典元素及其与离散的摩尔斯理论的关系。现在，我们证明，在某些可驯服条件下，两个可覆盖或可壳的简单复合物的乘积可在一个驯服条件下携带摩尔斯摩尔斯式三角剖分，并且在一个barycentric细分后，任何瓷砖或炮击都会驯服。我们推断出，尺寸的封闭歧管的任何有限产物小于四个携带的摩尔斯式三角剖分，其关键和H-媒介是圆柱状的。我们还证明，莫尔斯瓷砖的H矢量在小于四个的尺寸上始终是圆柱状的，只要其关键载体是palindromic，h-vector在小于四个的情况下或在h薄层的情况下。
We recently defined a property of Morse shellability (and tileability) of finite simplicial complexes which extends the classical one and its relations with discrete Morse theory. We now prove that the product of two Morse tileable or shellable simplicial complexes carries Morse tileable or shellable triangulations under some tameness condition, and that any tiling or shelling becomes tame after one barycentric subdivision. We deduce that any finite product of closed manifolds of dimensions less than four carries Morse shellable triangulations whose critical and h-vectors are palindromic. We also prove that the h-vector of a Morse tiling is always palindromic in dimension less than four or in the case of an h-tiling, provided its critical vector is palindromic.
