论文标题
明显表面的非交叉分区
Noncrossing partitions of a marked surface
论文作者
论文摘要
我们定义没有穿刺的标记表面的非交叉分区（内部标记点）。我们表明，非交叉分区的自然部分顺序是一个分级的晶格，并从拓扑上描述其等级函数。晶格中的较低间隔与其他表面的非交叉分区晶格产物是同构的。我们类似地定义了具有双点的对称标记表面的非交叉分区，并证明了一些类似的结果。对称性和双点的结合起着可能被穿刺发挥的作用。
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures.
