---
_id: '1022'
abstract:
- lang: eng
text: We introduce a multiscale topological description of the Megaparsec web-like
cosmic matter distribution. Betti numbers and topological persistence offer a
powerful means of describing the rich connectivity structure of the cosmic web
and of its multiscale arrangement of matter and galaxies. Emanating from algebraic
topology and Morse theory, Betti numbers and persistence diagrams represent an
extension and deepening of the cosmologically familiar topological genus measure
and the related geometric Minkowski functionals. In addition to a description
of the mathematical background, this study presents the computational procedure
for computing Betti numbers and persistence diagrams for density field filtrations.
The field may be computed starting from a discrete spatial distribution of galaxies
or simulation particles. The main emphasis of this study concerns an extensive
and systematic exploration of the imprint of different web-like morphologies and
different levels of multiscale clustering in the corresponding computed Betti
numbers and persistence diagrams. To this end, we use Voronoi clustering models
as templates for a rich variety of web-like configurations and the fractal-like
Soneira-Peebles models exemplify a range of multiscale configurations. We have
identified the clear imprint of cluster nodes, filaments, walls, and voids in
persistence diagrams, along with that of the nested hierarchy of structures in
multiscale point distributions. We conclude by outlining the potential of persistent
topology for understanding the connectivity structure of the cosmic web, in large
simulations of cosmic structure formation and in the challenging context of the
observed galaxy distribution in large galaxy surveys.
acknowledgement: Part of this work has been supported by the 7th Framework Programme
for Research of the European Commission, under FETOpen grant number 255827 (CGL
Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random
Systems via Algebraic Topology) number 320422.
article_processing_charge: No
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Bernard
full_name: Jones, Bernard
last_name: Jones
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic
web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical
Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862
apa: Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M.,
Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms
of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society.
Oxford University Press. https://doi.org/10.1093/mnras/stw2862
chicago: Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter,
Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic
Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical
Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.
ieee: P. Pranav et al., “The topology of the cosmic web in terms of persistent
Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4. Oxford University Press, pp. 4281–4310, 2017.
ista: Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B,
Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti
numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.
mla: Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent
Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.
short: P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B.
Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017)
4281–4310.
date_created: 2018-12-11T11:49:44Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-22T09:40:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/mnras/stw2862
external_id:
isi:
- '000395170200039'
intvolume: ' 465'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.04519
month: '01'
oa: 1
oa_version: Submitted Version
page: 4281 - 4310
publication: Monthly Notices of the Royal Astronomical Society
publication_identifier:
issn:
- '00358711'
publication_status: published
publisher: Oxford University Press
publist_id: '6373'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The topology of the cosmic web in terms of persistent Betti numbers
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 465
year: '2017'
...