论文标题
$ b $ - 物业的界限是几乎是pogorelov polytope
$B$-rigidity of the property to be an almost Pogorelov polytope
论文作者
论文摘要
复曲面拓扑分配给每个$ n $二维的组合简单凸polytope $ p $带$ m $ facets a $（m+n）$ - 尺寸瞬间瞬间 - 角度歧管$ \ nathcal {z} _p $，用紧凑型t^m $ t^m $ \ nathcal type typer typer typer of $ P $。我们研究了$ b $ - 关系的概念。 polytope $ p $的属性称为$ b $ -rigid，如果有任何分级环$ h^*的同构性，\ mathcal {z} _p，\ mathbb z）= h^*（\ mathcal {z} _q，_q，_q，\ mathbb z）$ for Simple $ n $ n $ -polytope $ polyies $ q $ q $ q q $ q q $ q q $ q q q ostimes。我们研究由$ 3 $维的多型家庭的家庭循环$ k $ - 边缘连接性定义的。这些家族包括旗帜多型和pogorelov的多面体，即可以实现的多面体作为Lobachevsky Space $ \ Mathbb l^3 $中的有界的右角式多型。 Pogorelov的多面体包括富勒烯 - 仅具有五角形和六角形面的简单多型。众所周知，要标记的属性和pogorelov polytope是$ b $ rigid。我们专注于几乎是pogorelov的多面体，它们在$ 4 $ edged的多台面上都非常周期性。它们对应于$ \ mathbb l^3 $中有限卷的右角层。有一个理想的亚科几乎几乎是pogorelov的多面体，对应于理想的右角多型。我们证明，这些属性几乎是Pogorelov polytope，而理想的几乎是Pogorelov polytope是$ b $ rigid。作为推论，我们获得了$ 3 $二维的AssociaHedron $ as^3 $和PermutoheDron $ pe^3 $是$ b $ rigid。我们概括了针对Pogorelov多面体已知的方法。我们在$ h^*（\ Mathcal {z} _p，\ Mathbb z）$中获得$ b $ - 条件的结果，并证明了所谓的可分离电路条件（SCC）的类似物。作为一个例子，我们考虑戒指$ h^*（\ Mathcal {z} _ {as^3}，\ Mathbb z）$。
Toric topology assigns to each $n$-dimensional combinatorial simple convex polytope $P$ with $m$ facets an $(m+n)$-dimensional moment-angle manifold $\mathcal{Z}_P$ with an action of a compact torus $T^m$ such that $\mathcal{Z}_P/T^m$ is a convex polytope of combinatorial type $P$. We study the notion of $B$-rigidity. A property of a polytope $P$ is called $B$-rigid, if any isomorphism of graded rings $H^*(\mathcal{Z}_P,\mathbb Z)= H^*(\mathcal{Z}_Q,\mathbb Z)$ for a simple $n$-polytope $Q$ implies that it also has this property. We study families of $3$-dimensional polytopes defined by their cyclic $k$-edge-connectivity. These families include flag polytopes and Pogorelov polytopes, that is polytopes realizable as bounded right-angled polytopes in Lobachevsky space $\mathbb L^3$. Pogorelov polytopes include fullerenes -- simple polytopes with only pentagonal and hexagonal faces. It is known that the properties to be flag and Pogorelov polytope are $B$-rigid. We focus on almost Pogorelov polytopes, which are strongly cyclically $4$-edge-connected polytopes. They correspond to right-angled polytopes of finite volume in $\mathbb L^3$. There is a subfamily of ideal almost Pogorelov polytopes corresponding to ideal right-angled polytopes. We prove that the properties to be an almost Pogorelov polytope and an ideal almost Pogorelov polytope are $B$-rigid. As a corollary we obtain that $3$-dimensional associahedron $As^3$ and permutohedron $Pe^3$ are $B$-rigid. We generalize methods known for Pogorelov polytopes. We obtain results on $B$-rigidity of subsets in $H^*(\mathcal{Z}_P,\mathbb Z)$ and prove an analog of the so-called separable circuit condition (SCC). As an example we consider the ring $H^*(\mathcal{Z}_{As^3},\mathbb Z)$.
