论文标题
磁盘和无k平等空间中磁盘的一般表示稳定性
Generalized representation stability for disks in a strip and no-k-equal spaces
论文作者
论文摘要
对于固定的J和W，我们研究了无限宽度w中n个标记的宽度1的标记磁盘的配置空间的同源性。随着n的成长，同源群体成倍增长，表明教会定义的广义代表稳定性 - 埃伦贝格（Ellenberg-Farb）和拉莫斯（Ramos）。我们证明了宽度2条带的这种广义表示稳定性，留下了w> 2的情况。我们还证明了该线路中的n个标记点的配置空间，其中无k是相等的。
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.
