{"paper":{"title":"SKK groups of manifolds and non-unitary invertible TQFTs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.AT","authors_text":"Luuk Stehouwer, Renee S. Hoekzema, Simona Vesel\\'a","submitted_at":"2025-04-10T17:32:26Z","abstract_excerpt":"This work considers the computation of controllable cut-and-paste groups $\\mathrm{SKK}^{\\xi}_n$ of manifolds with tangential structure $\\xi:B_n\\to BO_n$. To this end, we apply the work of Galatius-Madsen-Tillman-Weiss, Genauer and Schommer-Pries, who showed that for a wide range of structures $\\xi$ these groups fit into a short exact sequence that relates them to bordism groups of $\\xi$-manifolds with kernel generated by the disc-bounding $\\xi$-sphere. The order of this sphere can be computed by knowing the possible values of the Euler characteristic of $\\xi$-manifolds. We are thus led to addr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07917","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/2504.07917/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"}