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arXiv · 2107.04574

Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories

Hannah Alpert·Fedor Manin
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Abstract

We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way these spaces evolve both as $n$ increases (using the framework of representation stability) and as $w$ increases (using the framework of persistent homology). Finally, we include some results about the cup product in the cohomology and about the configuration space of unordered disks.

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BibTeXRIS

Hannah Alpert, Fedor Manin. 2021-07-09. Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories. https://doi.org/10.2140/gt.2024.28.641

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