非k-相等空间中圆盘的广义表示稳定性
Generalized representation stability for disks in a strip and no-k-equal spaces
摘要：
对于固定的j和w，我们研究了宽度为w的无限条中宽度为1的n个标号圆盘的位形空间的j次同调。随着n的增长，同调群的秩呈指数增长，这表明了Church-Ellenberg-Farb和Ramos定义的广义表示稳定性。我们证明了这种广义表示稳定的宽度为2的带，离开开放的情况下，w > 2。我们还证明了它的配置空间中的n个标记点的线，其中没有k是相等的。
英文摘要：
For fixed j and w, we study the j-th homology of the configuration space of n labeled disks of width 1 in an infinite strip of width w. As n grows, the homology groups grow exponentially in rank, suggesting a generalized representation stability as defined by Church--Ellenberg--Farb and Ramos. We prove this generalized representation stability for the strip of width 2, leaving open the case of w > 2. We also prove it for the configuration space of n labeled points in the line, of which no k are equal.
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