{"paper":{"title":"McClure-Smith cosimplicial machinery and the cacti operad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Paul Arnaud Songhafouo Tsopm\\'en\\'e","submitted_at":"2014-03-28T19:29:56Z","abstract_excerpt":"McClure and Smith constructed a functor that sends a topological multiplicative operad O to an E_2 algebra TotO. They define in fact an operad D_2 (acting on the totalization TotO) weakly equivalent to the little 2-disks operad. On the other hand, Salvatore showed that D_2 is isomorphic to the cacti operad MS, which has a nice geometric description. He also built a geometric action of MS on TotO. In this paper we detail the McClure-Smith action and the cacti action. Our main result says that they are compatible in the sense that some squares must commute."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7504","kind":"arxiv","version":1},"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"}