{"paper":{"title":"Multiplicative Structure in the Stable Splitting of $\\Omega SL_n(\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.AT","authors_text":"Allen Yuan, Jeremy Hahn","submitted_at":"2017-10-15T17:42:53Z","abstract_excerpt":"The space of based loops in $SL_n(\\mathbb{C})$, also known as the affine Grassmannian of $SL_n(\\mathbb{C})$, admits an $\\mathbb{E}_2$ or fusion product. Work of Mitchell and Richter proves that this based loop space stably splits as an infinite wedge sum. We prove that the Mitchell--Richter splitting is coherently multiplicative, but not $\\mathbb{E}_2$. Nonetheless, we show that the splitting becomes $\\mathbb{E}_2$ after base-change to complex cobordism. Our proof of the $\\mathbb{A}_\\infty$ splitting involves on the one hand an analysis of the multiplicative properties of Weiss calculus, and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05366","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"}