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

Hannah Alpert and Fedor Manin

Geometry & Topology 28 (2024) 641–699
Abstract

We give –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.

Keywords
configuration space, pure braid group, representation stability, twisted commutative algebra, permutohedron, discrete Morse theory, persistent homology, motion planning
Mathematical Subject Classification
Primary: 55R80
Secondary: 16S15, 18A25, 55N31, 57Q70
References
Publication
Received: 13 July 2021
Revised: 9 June 2022
Accepted: 30 September 2022
Published: 13 March 2024
Proposed: Benson Farb
Seconded: David Fisher, Mladen Bestvina
Authors
Hannah Alpert
Department of Mathematics and Statistics
Auburn University
Auburn, AL
United States
http://webhome.auburn.edu/~hca0013/
Fedor Manin
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA
United States
http://web.math.ucsb.edu/~manin/

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