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Higher interpolation and extension for persistence modules

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...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1137/16M1100472

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More from this funder
Name:
Engineering and Physical Sciences Research Council
Funding agency for:
Nanada, V
Grant:
EP/N510129/1
More from this funder
Name:
Air Force Office of Scientific Research
Funding agency for:
Bubenik, P
Grant:
FA9550-13-1-0115
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Applied Algebra and Geometry More from this journal
Volume:
1
Issue:
1
Pages:
272-284
Publication date:
2017-06-07
Acceptance date:
2017-03-27
DOI:
Keywords:
Pubs id:
pubs:700961
UUID:
uuid:cf3cd748-f1e1-454f-9dab-6b86ae56aa79
Local pid:
pubs:700961
Source identifiers:
700961
Deposit date:
2017-06-16

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