Author
Bubenik, P
de Silva, V
Nanada, V
Journal title
SIAM Journal on Applied Algebra and Geometry
DOI
10.1137/16M1100472
Issue
1
Volume
1
Last updated
2022-07-31T17:08:48.997+01:00
Page
272-284
Abstract
The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a coherence criterion which guarantees the extensibility of nonexpansive maps into this space across embeddings of the domain to larger ambient metric spaces. Our coherence criterion is category-theoretic, allowing Kan extensions to provide the desired extensions. Our main construction gives an isometric embedding of a metric space into the metric space of persistence modules with values in the spacetime of this metric space. As a consequence of such “higher interpolation,” it becomes possible to compare Vietoris–Rips and Cech complexes built ˇ within the space of persistence modules.
Symplectic ID
700961
Favourite
Off
Publication type
Journal Article
Publication date
07 Jun 2017
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