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

Alpert, Hannah¹ ; Manin, Fedor²

¹ Department of Mathematics and Statistics, Auburn University, Auburn, AL, United States
² Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States

Geometry & topology, Tome 28 (2024) no. 2, pp. 641-699.

Résumé

We give $\mathbb{Z}$–bases for the homology and cohomology of the configuration space 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.

Détail

DOI : 10.2140/gt.2024.28.641

Keywords: configuration space, pure braid group, representation stability, twisted commutative algebra, permutohedron, discrete Morse theory, persistent homology, motion planning

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