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Sketches of a platypus: persistent homology and its algebraic foundations
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. Jozef Stefan Inst, Slovenia.ORCID iD: 0000-0001-6322-7542
2014 (English)In: ALGEBRAIC TOPOLOGY: APPLICATIONS AND NEW DIRECTIONS, American Mathematical Society (AMS), 2014, 295-320 p.Conference paper (Refereed)
Abstract [en]

The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are rooted in choosing a particular algebraic foundational theory to describe persistent homology, and applying results from that theory to prove useful and important results.

In this survey paper, we shall examine the various choices in use, and what they allow us to prove. We shall also discuss the inherent differences between the choices people use, and speculate on potential directions of research to resolve these differences.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2014. 295-320 p.
, Contemporary Mathematics, ISSN 0271-4132 ; 620
National Category
Algebra and Logic Computational Mathematics
URN: urn:nbn:se:kth:diva-150369DOI: 10.1090/conm/620/12371ISI: 000361089400013ISBN: 978-1-4704-1855-7OAI: diva2:742582
Standford Symposium on Algebraic Topology: Applications and New Directions, JUL 23-27, 2012
EU, FP7, Seventh Framework Programme

QC 20151005

Available from: 2014-09-02 Created: 2014-09-02 Last updated: 2015-10-05Bibliographically approved

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Vejdemo-Johansson, Mikael
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