{"paper":{"title":"Real spin bordism and orientations of topological $\\mathrm{K}$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Yigal Kamel, Zachary Halladay","submitted_at":"2024-05-02T03:02:05Z","abstract_excerpt":"We construct a commutative orthogonal $C_2$-ring spectrum, $\\mathrm{MSpin}^c_{\\mathbb{R}}$, along with a $C_2$-$E_{\\infty}$-orientation $\\mathrm{MSpin}^c_{\\mathbb{R}} \\to \\mathrm{KU}_{\\mathbb{R}}$ of Atiyah's Real K-theory. Further, we define $E_{\\infty}$-maps $\\mathrm{MSpin} \\to (\\mathrm{MSpin}^c_{\\mathbb{R}})^{C_2}$ and $\\mathrm{MU}_{\\mathbb{R}} \\to \\mathrm{MSpin}^c_{\\mathbb{R}}$, which are used to recover the three well-known orientations of topological $\\mathrm{K}$-theory, $\\mathrm{MSpin}^c \\to \\mathrm{KU}$, $\\mathrm{MSpin} \\to \\mathrm{KO}$, and $\\mathrm{MU}_{\\mathbb{R}} \\to \\mathrm{KU}_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.00963","kind":"arxiv","version":2},"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/2405.00963/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"}