论文标题
镜像拓扑posets的UP拓扑
The Up Topology for Mirrored Topological Posets
论文作者
论文摘要
对于离散的POSET $ \ MATHCAL X $，McCord证明了自然地图$ | {\ Mathcal X} | \ to {\ Mathcal X} $，从订单复杂到使用UP TOUSOLOGY的POSET，是一个弱的同型等价。不久之后，乌西瓦耶维奇（Uzivaljević）定义了拓扑poset的秩序复杂概念。对于大量这样的拓扑作用，我们证明了麦考德定理的类似物，即，从阶络合物到拓扑质量poset的自然图具有UP拓扑结构，是一个弱同质性等效性。一个例子是$ \ r^{n+1} $的适当非零线性子空间的Grassmann Poset。在这里，Vassiliev计算了阶络合物的同喻类型。我们的定理允许我们将这些信息（最多达到弱同质型）转移到Grassmann Poset上，并具有UP拓扑结构。
For a discrete poset $\mathcal X$, McCord proved that the natural map $|{\mathcal X}|\to {\mathcal X}$, from the order complex to the poset with the Up topology, is a weak homotopy equivalence. Much later, uZivaljević defined the notion of order complex for a topological poset. For a large class of such topological posets we prove the analog of McCord's theorem, namely that the natural map from the order complex to the topological poset with the Up topology is a weak homotopy equivalence. An example is the Grassmann poset of proper non-zero linear subspaces of $\R^{n+1}$. Here, Vassiliev had computed the homotopy type of the order complex. Our theorem allows us to transfer that information (up to weak homotopy type) to the Grassmann poset itself with the Up topology.
