{"paper":{"title":"Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Guoliang Yu, Jianchao Wu, Liang Guo, Qin Wang","submitted_at":"2024-11-27T17:35:53Z","abstract_excerpt":"The equivariant coarse Novikov conjectures stand among a handful profound $K$-theoretic conjectures in noncommutative geometry. Motivated by the quest to verify Novikov-type conjectures for groups of diffeomorphisms, we study in this paper the equivariant coarse Novikov conjectures for spaces that equivariantly and coarsely embed into admissible Hilbert-Hadamard spaces, which are a type of infinite-dimensional nonpositively curved spaces. The paper is split into two parts.\n  We prove in the first part that for any metric space $X$ with bounded geometry and with a proper isometric action $\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18538","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}