{"paper":{"title":"On the metalinear algebraic cobordism spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AT","authors_text":"Ahina Nandy, Egor Zolotarev","submitted_at":"2026-06-10T12:26:27Z","abstract_excerpt":"In this paper, we study the metalinear algebraic cobordism spectrum $\\mathrm{MML}$ (also sometimes denoted $\\mathrm{MSL}^c$), which is built from the structure groups of oriented vector bundles. We establish an interpolation between $\\mathrm{MSL}$ and $\\mathrm{MML}$ and deduce that the canonical morphism $\\mathrm{MSL}\\to \\mathrm{MML}$ admits a retraction. We parametrize all such retractions in the category of $\\mathrm{MSL}$-modules and, after fixing one of them, obtain an equivalence $\\mathrm{MML}\\cong\\mathrm{MSL}\\oplus \\Sigma^{2,1}\\mathrm{MGL}$. As an application of these results, we determin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12001","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/2606.12001/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"}