Decomposition of pointwise finite-dimensional persistence modules

被引：86

作者：

Crawley-Boevey, William ^{[1
]}

机构：

[1] Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 05期

关键词：

Persistence module; persistent homology;

D O I：

10.1142/S0219498815500668

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on images and kernels.

引用

页数：8

共 11 条

[1]

[Anonymous], ARXIV12073674

[2]

Carlsson G., 2004, Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, DOI [DOI 10.1145/1057432.1057449, DOI 10.1142/S0218654305000761, 10.1142/S0218654305000761]

[3] Persistence stability for geometric complexes [J].

Chazal, Frederic ;

de Silva, Vin ;

Oudot, Steve .

GEOMETRIAE DEDICATA, 2014, 173 (01) :193-214

[4] Proximity of Persistence Modules and their Diagrams [J].

Chazal, Frederic ;

Cohen-Steiner, David ;

Glisse, Marc ;

Guibas, Leonidas J. ;

Oudot, Steve Y. .

PROCEEDINGS OF THE TWENTY-FIFTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SCG'09), 2009, :237-246

[5] LOCALLY FINITELY PRESENTED ADDITIVE CATEGORIES [J].

CRAWLEYBOEVEY, W .

COMMUNICATIONS IN ALGEBRA, 1994, 22 (05) :1641-1674

[6] Barcodes: The persistent topology of data [J].

Ghrist, Robert .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 45 (01) :61-75

[7]

Grothendieck A., 1961, Publ. Math-Paris, V11, P5

[8]

Lesnick M, 2011, ARXIV11065305

[9] INDECOMPOSABLE REPRESENTATIONS OF DIHEDRAL 2-GROUPS [J].

RINGEL, CM .

MATHEMATISCHE ANNALEN, 1975, 214 (01) :19-34

[10]

WEBB C, 1985, P AM MATH SOC, V94, P565

← 1 2 →