article published yes Pratyush Pranav author Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Rien Van De Weygaert author Gert Vegter author Michael Kerber author Bernard Jones author Mathijs Wintraecken author 307CFBC8-F248-11E8-B48F-1D18A9856A870000-0002-7472-2220 HeEd department 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. Oxford University Press2017 eng 0035-8711 1608.04519 00039517020003910.1093/mnras/stw2862 46544281 - 4310 P. Pranav <i>et al.</i>, “The topology of the cosmic web in terms of persistent Betti numbers,” <i>Monthly Notices of the Royal Astronomical Society</i>, vol. 465, no. 4. Oxford University Press, pp. 4281–4310, 2017. Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. <i>Monthly Notices of the Royal Astronomical Society</i>. 2017;465(4):4281-4310. doi:<a href="https://doi.org/10.1093/mnras/stw2862">10.1093/mnras/stw2862</a> Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M., Jones, B., &#38; Wintraecken, M. (2017). The topology of the cosmic web in terms of persistent Betti numbers. <i>Monthly Notices of the Royal Astronomical Society</i>. Oxford University Press. <a href="https://doi.org/10.1093/mnras/stw2862">https://doi.org/10.1093/mnras/stw2862</a> 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.” <i>Monthly Notices of the Royal Astronomical Society</i>. Oxford University Press, 2017. <a href="https://doi.org/10.1093/mnras/stw2862">https://doi.org/10.1093/mnras/stw2862</a>. Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” <i>Monthly Notices of the Royal Astronomical Society</i>, vol. 465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:<a href="https://doi.org/10.1093/mnras/stw2862">10.1093/mnras/stw2862</a>. 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. 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. 10222018-12-11T11:49:44Z2025-06-04T08:10:31Z