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A
$K$-theory spectrum for cobordism cut and paste groups
Renee S Hoekzema, Carmen Rovi and Julia Semikina |
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Algebraic & Geometric Topology 25 (2025) 3287–3314
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Abstract |
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Cobordism groups and cut and paste groups of manifolds arise from imposing two different relations on the monoid of manifolds under disjoint union. By imposing both relations simultaneously, a cobordism cut and paste group is defined. We extend this definition to manifolds with boundary, obtaining the group , and study the relationship of the group to an appropriately defined cobordism group of manifolds with boundary. The main results are the construction of a spectrum that recovers on the cobordism cut and paste groups of manifolds with boundary, , and a map of spectra that lifts the canonical quotient map . |
Keywords
scissors congruence, cobordism, $K$-theory, categories
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Mathematical Subject Classification
Primary: 18D99, 18F25, 18F30, 19D99, 57N70
Secondary: 55P15, 57N40, 57R75, 57R90
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References |
Publication
Received: 3 October 2022
Revised: 12 June 2024
Accepted: 23 July 2024
Published: 1 October 2025
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Authors |
| Renee S Hoekzema | |
| Department of Mathematics Vrije Universiteit Amsterdam Amsterdam Netherlands |
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| Carmen Rovi | |
| Deptartment of Mathematics and
Statistics Loyola University Chicago Chicago, IL United States |
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| Julia Semikina | |
| Laboratoire Paul Painlevé Université de Lille Villeneuve d’Ascq France |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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