Geodesic
Homological approximations in persistence theory
Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 66-103

Voir la notice de l'article provenant de la source Cambridge

DOI

We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group generated by a finite set of indecomposable modules. We focus in particular on groups generated by “spread modules,” which are sometimes called “interval modules” in the persistence theory literature. We show that both the dimension vector and rank invariant are equivalent to homological invariants taking values in groups generated by spread modules. We also show that the free abelian group generated by the “single-source” spread modules gives rise to a new invariant which is finer than the rank invariant.
DOI : 10.4153/S0008414X22000657
Mots-clés : persistence modules, invariants, Grothendieck groups, relative homological algebra, exact structures 
Blanchette, Benjamin; Brüstle, Thomas; Hanson, Eric J. Homological approximations in persistence theory. Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 66-103. doi: 10.4153/S0008414X22000657
@article{10_4153_S0008414X22000657,
     author = {Blanchette, Benjamin and Br\"ustle, Thomas and Hanson, Eric J.},
     title = {Homological approximations in persistence theory},
     journal = {Canadian journal of mathematics},
     pages = {66--103},
     year = {2024},
     volume = {76},
     number = {1},
     doi = {10.4153/S0008414X22000657},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000657/}
}
TY  - JOUR
AU  - Blanchette, Benjamin
AU  - Brüstle, Thomas
AU  - Hanson, Eric J.
TI  - Homological approximations in persistence theory
JO  - Canadian journal of mathematics
PY  - 2024
SP  - 66
EP  - 103
VL  - 76
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000657/
DO  - 10.4153/S0008414X22000657
ID  - 10_4153_S0008414X22000657
ER  - 
%0 Journal Article
%A Blanchette, Benjamin
%A Brüstle, Thomas
%A Hanson, Eric J.
%T Homological approximations in persistence theory
%J Canadian journal of mathematics
%D 2024
%P 66-103
%V 76
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000657/
%R 10.4153/S0008414X22000657
%F 10_4153_S0008414X22000657

Cité par Sources :