Stratifications on the Ran Space

Janis Lazovskis* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We describe a partial order on finite simplicial complexes. This partial order provides a poset stratification of the product of the Ran space of a metric space and the nonnegative real numbers, through the Čech simplicial complex. We show that paths in this product space respecting its stratification induce simplicial maps between the endpoints of the path.
Original languageEnglish
Pages (from-to)143-158
Number of pages16
Early online date11 Jun 2021
Publication statusPublished - 1 Apr 2022

Bibliographical note

Acknowledgements: The author was partly sponsored by EP/P025072/1. Thanks to Ben Antieau and Shmuel Weinberger for insightful discussions and guidance. Thanks to Justin Curry for suggesting the counterexample of Fig. 4. Thanks to the reviewers for helpful comments and corrections.

Data Availability Statement

Data Availability: Data sharing not applicable to this article as no datasets were generated or analysed during
the current study.


  • Stratifications
  • Simplicial complexes
  • Configuration space
  • Entrance path


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