Approximate Triangulations of Grassmann Manifolds

被引：1

作者：

Knudson, Kevin P. ^{[1
]}

机构：

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

ALGORITHMS | 2020年 / 13卷 / 07期

关键词：

Grassmannian; persistent homology; Vietoris-Rips complex; witness complex; triangulation; EMBEDDINGS;

D O I：

10.3390/a13070172

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We define the notion of an approximate triangulation for a manifold M embedded in Euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in M and use persistent homology to find a complex in the family whose homology agrees with that of M. Our key examples are various Grassmann manifolds G(k) (R-n).

引用

页数：15

共 15 条

[1] Aanjaneya M., 2007, MACIS P
[2] There is no tame triangulation of the infinite real Grassmannian
Anderson, L
Davis, JF
[J]. ADVANCES IN APPLIED MATHEMATICS, 2001, 26 (03) : 226 - 236
[3] Casian L., 2013, PREPRINT
[4] Towards Persistence-Based Reconstruction in Euclidean Spaces
Chazal, Frederic
Oudot, Steve Y.
[J]. PROCEEDINGS OF THE TWENTY-FOURTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SGG'08), 2008, : 232 - 241
[5] Davis DM, 1998, BOL SOC MAT MEX, V4, P115
[6] de Silva V., 2004, SPBG 04 S POINT BAS
[7] Duan H., ARXIV200313125
[8] Eirene Henselman G., SOFTWARE PACKAGE COM
[9] Govc D., ARXIV200108292
[10] MILNOR J, 1974, ANN MATH STUDIES, V76

← 1 2 →