Geodesic
Alexander duality for parametrized homology
Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 227-243.

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

Parametrized homology is a variant of zigzag persistent homology that measures how the homology of the level sets of the space changes as we vary the parameter. This paper extends Alexander Duality to this setting. Let $X \subset \mathbb{R}^n \times \mathbb{R}$ with $n\geq 2$ be a compact set satisfying certain conditions, let $Y = (\mathbb{R}^n \times \mathbb{R}) \setminus X$, and let $p$ be the projection onto the second factor. Both $X$ and $Y$ are parametrized spaces with respect to the projection. We show that if $(X, p|_X)$ has a well-defined parametrized homology, then the pair $(Y, p|_Y)$ has a well-defined reduced parametrized homology. We also establish a relationship between the parametrized homology of $(X, p|_X)$ and the reduced parametrized homology of $(Y, p|_Y)$.
DOI : 10.4310/HHA.2013.v15.n2.a14
Classification : 55N05, 55U30
Keywords: Alexander duality, persistent homology, zigzag persistence, levelset zigzag persistence 
@article{HHA_2013_15_2_a13,
     author = {Sara Kali\v{s}nik},
     title = {Alexander duality for parametrized homology},
     journal = {Homology, homotopy, and applications},
     pages = {227--243},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     doi = {10.4310/HHA.2013.v15.n2.a14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a14/}
}
TY  - JOUR
AU  - Sara Kališnik
TI  - Alexander duality for parametrized homology
JO  - Homology, homotopy, and applications
PY  - 2013
SP  - 227
EP  - 243
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a14/
DO  - 10.4310/HHA.2013.v15.n2.a14
LA  - en
ID  - HHA_2013_15_2_a13
ER  - 
%0 Journal Article
%A Sara Kališnik
%T Alexander duality for parametrized homology
%J Homology, homotopy, and applications
%D 2013
%P 227-243
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a14/
%R 10.4310/HHA.2013.v15.n2.a14
%G en
%F HHA_2013_15_2_a13
Sara Kališnik. Alexander duality for parametrized homology. Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 227-243. doi : 10.4310/HHA.2013.v15.n2.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a14/

Cité par Sources :