Year: 2016
Type: article
Abstract: There are two interesting families of E 2 {E_{2}} -operads, those that detect double loop spaces, and those that solve Deligne’s conjecture on Hochschild cochains. The first family deformation retracts to Milgram’s model obtained by gluing together permutohedra along their faces. We show how the second family can be covered by permutohedra as well, shedding new light on several proposed solutions of Deligne’s conjecture. In particular, our approach induces an explicit homotopy equivalence between the models of the two families. The permutohedra and partial orders play a central role providing direct links to other fields of mathematics. We for instance find a new cellular decomposition of permutohedra using partial orders and that the permutohedra give the cells for the Dyer–Lashof operations.
Source: Forum Mathematicum
Authors: Ralph M. Kaufmann, Yongheng Zhang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Simons Foundation
Award: G4354308921
OpenAlex ID: W2280247020