Automorphisms of the little disks operad with torsion coefficients

2016/12/11 by Geoffroy Horel, Horel, Geoffroy
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1612.03420

openalex publication_date 2016/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the automorphisms of the Bousfield-Kan completion at a prime p of the little two-disks operads and show that they are given by the pro-p Grothendieck-Teichmüller group. We also show that the Grothendieck-Teichmüller group acts faithfully on the p-complete stable little disks operad.

Related

• Profinite completion of operads and the Grothendieck-Teichmüller group
• Every Endomorphism of the Framed Little Disk Operad is an Automorphism
• Automorphisms of framed operads
• Little discs operads, graph complexes and Grothendieck--Teichmüller groups
• Real models for the framed little n-disks operads