Stratifications on the Ran Space

Janis Lazovskis

doi:10.1007/s11083-021-09568-1

Stratifications on the Ran Space

Janis Lazovskis^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

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
Number of pages	16
Journal	Order
Early online date	11 Jun 2021
DOIs	https://doi.org/10.1007/s11083-021-09568-1
Publication status	E-pub ahead of print - 11 Jun 2021

Keywords

Stratifications
Simplicial complexes
Configuration space
Entrance path

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10.1007/s11083-021-09568-1Licence: CC BY

Cite this

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title = "Stratifications on the Ran Space",

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 {\v C}ech simplicial complex. We show that paths in this product space respecting its stratification induce simplicial maps between the endpoints of the path.",

keywords = "Stratifications, Simplicial complexes, Configuration space, Entrance path",

author = "Janis Lazovskis",

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. DataAvailability Data sharing not applicable to this article as no datasets were generated or analysed during the current study.",

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PY - 2021/6/11

Y1 - 2021/6/11

N2 - 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.

AB - 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.

KW - Stratifications

KW - Simplicial complexes

KW - Configuration space

KW - Entrance path

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M3 - Article

JO - Order

JF - Order

SN - 0167-8094

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Stratifications on the Ran Space

Abstract

Keywords

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