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K-theory of multiparameter persistence modules: Additivity.
- Source :
-
Proceedings of the American Mathematical Society, Series B . 3/5/2024, Vol. 11, p63-74. 12p. - Publication Year :
- 2024
-
Abstract
- Persistence modules stratify their underlying parameter space, a quality that makes persistence modules amenable to study via invariants of stratified spaces. In this article, we extend a result previously known only for one-parameter persistence modules to grid multiparameter persistence modules. Namely, we show the K-theory of grid multiparameter persistence modules is additive over strata. This is true for both standard monotone multi-parameter persistence as well as multiparameter notions of zig-zag persistence. We compare our calculations for the specific group K_0 with the recent work of Botnan, Oppermann, and Oudot, highlighting and explaining the differences between our results through an explicit projection map between computed groups. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MAP projection
*K-theory
Subjects
Details
- Language :
- English
- ISSN :
- 23301511
- Volume :
- 11
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society, Series B
- Publication Type :
- Academic Journal
- Accession number :
- 175851234
- Full Text :
- https://doi.org/10.1090/bproc/208