Foundations of Computational Mathematics

, Volume 10, Issue 4, pp 367-405

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Zigzag Persistence

  • Gunnar CarlssonAffiliated withDepartment of Mathematics, Stanford University Email author 
  • , Vin de SilvaAffiliated withDepartment of Mathematics, Pomona College


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