Foundations of Computational Mathematics

, Volume 10, Issue 4, pp 367–405

Zigzag Persistence

Open Access

DOI: 10.1007/s10208-010-9066-0

Cite this article as:
Carlsson, G. & de Silva, V. Found Comput Math (2010) 10: 367. doi:10.1007/s10208-010-9066-0


We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop theoretical and algorithmic foundations with a view towards applications in topological statistics.


Applied topology Persistent topology Quiver representations 

Mathematics Subject Classification (2000)

68W30 55N99 
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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsPomona CollegeClaremontUSA

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