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arXiv · 1403.7504

McClure-Smith cosimplicial machinery and the cacti operad

Paul Arnaud Songhafouo Tsopméné
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Abstract

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.

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Paul Arnaud Songhafouo Tsopméné. 2014-03-28. McClure-Smith cosimplicial machinery and the cacti operad. https://arxiv.org/abs/1403.7504

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