{"paper":{"title":"Some properties of the Thom spectrum over loop suspension of complex projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrew Baker, Birgit Richter","submitted_at":"2012-07-20T13:31:34Z","abstract_excerpt":"This note provides a reference for some properties of the Thom spectrum $M\\xi$ over $\\Omega\\Sigma\\CPi$. Some of this material is used in recent work of Kitchloo and Morava. We determine the $M\\xi$-cohomology of $\\CPi$ and show that $M\\xi^*(\\CPi)$ injects into power series over the algebra of non-symmetric functions. We show that $M\\xi$ gives rise to a commutative formal group law over the non-commutative ring $\\pi_*M\\xi$. We also discuss how $M\\xi$ and some real and quaternionic analogues behave with respect to spectra that are related to these Thom spectra by splittings and by maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4947","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":""},"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"}