{"paper":{"title":"Infinite Loop Spaces and Group Actions on Strongly Self-Absorbing C*-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.AT","authors_text":"George Tridimas, Ulrich Pennig","submitted_at":"2026-07-22T13:02:19Z","abstract_excerpt":"Lifting obstructions for group actions, cocycle actions, and $\\Gamma$-kernels admit a cohomological description via topological crossed modules, as recently developed by Izumi, Giron-Pacheco, and the first named author. For a strongly self-absorbing $C^*$-algebra $A$, we show that the classifying spaces $\\mathcal{B}^D\\mathcal{G}_A$ and $\\mathcal{B}^DP\\mathcal{G}_A$ of the respective crossed modules governing cocycle actions and $\\Gamma$-kernels, respectively, carry infinite loop space structures induced by the tensor product; the same holds for the crossed module $B^D\\tilde{\\mathcal{G}}_A$ whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20105","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/2607.20105/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"}