Abstract
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 language | English |
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Pages (from-to) | 143-158 |
Number of pages | 16 |
Journal | Order |
Volume | 39 |
Early online date | 11 Jun 2021 |
DOIs | |
Publication status | Published - 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 duringthe current study.
Keywords
- Stratifications
- Simplicial complexes
- Configuration space
- Entrance path