| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4658246 | Topology and its Applications | 2015 | 20 Pages |
Abstract
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.
- . 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Paul Arnaud Songhafouo Tsopméné,