{"paper":{"title":"De Rham cohomology of configuration spaces with Poisson measure","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"A. Daletskii, E. Lytvynov, S. Albeverio","submitted_at":"2006-08-14T13:13:00Z","abstract_excerpt":"The space $\\Gamma_X$ of all locally finite configurations in a\n Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $\\Gamma_X$, equipped with the Poisson measure, and the corresponding deRham cohomology are studied. The latter is shown to be unitarily isomorphic to a certain Hilbert tensor algebra generated by the $L^2$-cohomology of the underlying manifold $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608338","kind":"arxiv","version":1},"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"}