Automorphisms of framed operads

2024/03/17 by Horel, Geoffroy, Willwacher, Thomas
#Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2403.11185

Abstract

Let \mathsf P be an operad acted upon by a group G, and let \mathsf Q=\mathsf P\rtimes G be the corresponding framed operad. We relate the homotopy automorphism groups of \mathsf P and \mathsf Q. We apply the result to compute the automorphisms of the framed little disks operad.

Related

• Every Endomorphism of the Framed Little Disk Operad is an Automorphism
• Automorphisms of the little disks operad with torsion coefficients
• Profinite completion of operads and the Grothendieck-Teichmüller group
• Homotopy derivations of the framed little discs operads
• Real models for the framed little n-disks operads