{"paper":{"title":"Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","math.AT"],"primary_cat":"astro-ph.CO","authors_text":"Bernard J.T. Jones, Changbom Park, Gert Vegter, Job Feldbrugge, Michael Kerber, Pratyush Pranav, Rien van de Weygaert, Robert J. Adler, Thomas Buchert","submitted_at":"2018-12-18T11:41:03Z","abstract_excerpt":"This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers $\\beta_0$, $\\beta_1$ and $\\beta_2$. We show that Betti numbers entail a considerably richer characterization of the topology of the primordial density field. Of particular interest is that Betti numbers specify which topological features - islands, cavities or tunnels - define its spatial structure.\n  A principal characteristic of Gaussian fields is that the three Betti numbers dominate the topology at different density ranges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07310","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}