2014/03/28 by Paul Arnaud Songhafouo Tsopméné, Tsopméné, Paul Arnaud Songhafouo
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18D50
paper · pdf · doi:10.48550/arxiv.1403.7504
16 pages, 3 figures
arxiv created 2014/03/28 · arxiv updated 2014/03/31
McClure and Smith constructed a functor that sends a topological multiplicative operad O to an E2 algebra TotO. They define in fact an operad D2 (acting on the totalization TotO) weakly equivalent to the little 2-disks operad. On the other hand, Salvatore showed that D2 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.