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Configuration spaces of
disks in a strip, twisted algebras, persistence, and other
stories
Hannah Alpert and Fedor Manin |
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Geometry & Topology 28 (2024) 641–699
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Abstract |
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We give –bases for the homology and cohomology of the configuration space of unit disks in an infinite strip of width , first studied by Alpert, Kahle and MacPherson. We also study the way these spaces evolve both as increases (using the framework of representation stability) and as 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
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Mathematical Subject Classification
Primary: 55R80
Secondary: 16S15, 18A25, 55N31, 57Q70
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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
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Authors |
| Hannah Alpert | |
| Department of Mathematics and
Statistics Auburn University Auburn, AL United States |
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| http://webhome.auburn.edu/~hca0013/ | |
| Fedor Manin | |
| Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
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| http://web.math.ucsb.edu/~manin/ | |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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