Geodesic
Zig-zag modules: cosheaves and $k$-theory
Homology, homotopy, and applications, Tome 25 (2023) no. 2, pp. 243-274.

Voir la notice de l'article provenant de la source International Press of Boston

Persistence modules have a natural home in the setting of stratified spaces and constructible cosheaves. In this article, we first give explicit constructible cosheaves for common data-motivated persistence modules, namely, for modules that arise from zig‑zag filtrations (including monotone filtrations), and for augmented persistence modules (which encode the data of instantaneous events). We then identify an equivalence of categories between a particular notion of zig‑zag modules and the combinatorial entrance path category on stratified $\mathbb{R}$. Finally, we compute the algebraic $K$-theory of generalized zig‑zag modules and describe connections to both Euler curves and $K_0$ of the monoid of persistence diagrams as described by Bubenik and Elchesen.
DOI : 10.4310/HHA.2023.v25.n2.a11
Classification : 18F25, 19M05, 32S60
Keywords: persistence module, zig-zag persistence, cosheaf, algebraic $K$-theory 
@article{HHA_2023_25_2_a10,
     author = {Ryan Grady and Anna Schenfisch},
     title = {Zig-zag modules: cosheaves and $k$-theory},
     journal = {Homology, homotopy, and applications},
     pages = {243--274},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2023},
     doi = {10.4310/HHA.2023.v25.n2.a11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a11/}
}
TY  - JOUR
AU  - Ryan Grady
AU  - Anna Schenfisch
TI  - Zig-zag modules: cosheaves and $k$-theory
JO  - Homology, homotopy, and applications
PY  - 2023
SP  - 243
EP  - 274
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a11/
DO  - 10.4310/HHA.2023.v25.n2.a11
LA  - en
ID  - HHA_2023_25_2_a10
ER  - 
%0 Journal Article
%A Ryan Grady
%A Anna Schenfisch
%T Zig-zag modules: cosheaves and $k$-theory
%J Homology, homotopy, and applications
%D 2023
%P 243-274
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a11/
%R 10.4310/HHA.2023.v25.n2.a11
%G en
%F HHA_2023_25_2_a10
Ryan Grady; Anna Schenfisch. Zig-zag modules: cosheaves and $k$-theory. Homology, homotopy, and applications, Tome 25 (2023) no. 2, pp. 243-274. doi : 10.4310/HHA.2023.v25.n2.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a11/

Cité par Sources :