{"paper":{"title":"Odd primary analogs of Real orientations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrew Senger, Dylan Wilson, Jeremy Hahn","submitted_at":"2020-09-27T00:33:37Z","abstract_excerpt":"We define, in $C_p$-equivariant homotopy theory for $p>2$, a notion of $\\mu_p$-orientation analogous to a $C_2$-equivariant Real orientation. The definition hinges on a $C_p$-space $\\mathbb{CP}^{\\infty}_{\\mu_p}$, which we prove to be homologically even in a sense generalizing recent $C_2$-equivariant work on conjugation spaces.\n  We prove that the height $p-1$ Morava $E$-theory is $\\mu_p$-oriented and that $\\mathrm{tmf}(2)$ is $\\mu_3$-oriented. We explain how a single equivariant map $v_1^{\\mu_p}:S^{2\\rho} \\to \\Sigma^{\\infty} \\mathbb{CP}^{\\infty}_{\\mu_p}$ completely generates the homotopy of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.12716","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/2009.12716/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"}