Hodge Theory on Metric Spaces

被引：16

作者：

Bartholdi, Laurent ^{[1
]}

Schick, Thomas ^{[1
]}

Smale, Nat ^{[2
]}

Smale, Steve ^{[3
]}

机构：

[1] Univ Gottingen, Gottingen, Germany

[2] Univ Utah, Salt Lake City, UT USA

[3] City Univ Hong Kong, Pokfulam, Peoples R China

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2012年 / 12卷 / 01期

关键词：

Hodge theory; L-2; cohomology; Metric spaces; Harmonic forms; Medium-scale geometry; L2-COHOMOLOGY;

D O I：

10.1007/s10208-011-9107-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Hodge theory is a beautiful synthesis of geometry, topology, and analysis which has been developed in the setting of Riemannian manifolds. However, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step toward understanding the geometry of vision. Appendix B by Anthony Baker discusses a separable, compact metric space with infinite-dimensional alpha-scale homology.

引用

页码：1 / 48

页数：48