Geodesic
Persistent homology with non-contractible preimages
Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 315-326.

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

For a fixed $N$, we analyze the space of all sequences $z=(z_1,\dotsc,z_N)$, approximating a continuous function on the circle, with a given persistence diagram $P$, and show that the typical components of this space are homotopy equivalent to $S^1$. We also consider the space of functions on $Y$-shaped (resp., starshaped) trees with a $2$-point persistence diagram, and show that this space is homotopy equivalent to $S^1$ (resp., to a bouquet of circles).
DOI : 10.4310/HHA.2022.v24.n2.a16
Classification : 55P15
Keywords: persistent homology, persistence diagram, homotopy, poset 
@article{HHA_2022_24_2_a15,
     author = {Konstantin Mischaikow and Charles Weibel},
     title = {Persistent homology with non-contractible preimages},
     journal = {Homology, homotopy, and applications},
     pages = {315--326},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2022},
     doi = {10.4310/HHA.2022.v24.n2.a16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a16/}
}
TY  - JOUR
AU  - Konstantin Mischaikow
AU  - Charles Weibel
TI  - Persistent homology with non-contractible preimages
JO  - Homology, homotopy, and applications
PY  - 2022
SP  - 315
EP  - 326
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a16/
DO  - 10.4310/HHA.2022.v24.n2.a16
LA  - en
ID  - HHA_2022_24_2_a15
ER  - 
%0 Journal Article
%A Konstantin Mischaikow
%A Charles Weibel
%T Persistent homology with non-contractible preimages
%J Homology, homotopy, and applications
%D 2022
%P 315-326
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a16/
%R 10.4310/HHA.2022.v24.n2.a16
%G en
%F HHA_2022_24_2_a15
Konstantin Mischaikow; Charles Weibel. Persistent homology with non-contractible preimages. Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 315-326. doi : 10.4310/HHA.2022.v24.n2.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a16/

Cité par Sources :