{"paper":{"title":"Bredon homological stability for configuration spaces of $G$-manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Chase Vogeli, Eva Belmont, J.D. Quigley","submitted_at":"2023-11-04T17:20:37Z","abstract_excerpt":"McDuff and Segal proved that unordered configuration spaces of open manifolds satisfy homological stability: there is a stabilization map $\\sigma: C_n(M)\\to C_{n+1}(M)$ which is an isomorphism on $H_d(-;\\mathbb{Z})$ for $n\\gg d$. For a finite group $G$ and an open $G$-manifold $M$, under some hypotheses we define a family of equivariant stabilization maps $\\sigma_{G/H}:C_n(M)\\to C_{n+|G/H|}(M)$ for $H\\leq G$. In general, these do not induce stability for Bredon homology, the equivariant analogue of singular homology. Instead, we show that each $\\sigma_{G/H}$ induces isomorphisms on the ordinar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02459","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.02459/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"}