McClure-Smith cosimplicial machinery and the cacti operad
Algebraic Topology
2014-03-31 v1
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.
Keywords
Cite
@article{arxiv.1403.7504,
title = {McClure-Smith cosimplicial machinery and the cacti operad},
author = {Paul Arnaud Songhafouo Tsopméné},
journal= {arXiv preprint arXiv:1403.7504},
year = {2014}
}
Comments
16 pages, 3 figures