{"paper":{"title":"On the $\\mathrm{EO}$-orientability of vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hood Chatham, Prasit Bhattacharya","submitted_at":"2020-03-08T15:07:26Z","abstract_excerpt":"We study the orientability of vector bundles with respect to a family of cohomology theories called $\\mathrm{EO}$-theories. The $\\mathrm{EO}$-theories are higher height analogues of real $\\mathrm{K}$-theory $\\mathrm{KO}$. For each $\\mathrm{EO}$-theory, we prove that the direct sum of $i$ copies of any vector bundle is $\\mathrm{EO}$-orientable for some specific integer $i$. Using a splitting principal, we reduce to the case of the canonical line bundle over $\\mathbb{CP}^{\\infty}$. Our method involves understanding the action of an order $p$ subgroup of the Morava stabilizer group on the Morava "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.03795","kind":"arxiv","version":3},"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/2003.03795/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"}