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arXiv · 2006.01240

Generalized representation stability for disks in a strip and no-k-equal spaces

Hannah Alpert
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Abstract

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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Hannah Alpert. 2020-06-01. Generalized representation stability for disks in a strip and no-k-equal spaces. https://arxiv.org/abs/2006.01240

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