Every Endomorphism of the Framed Little Disk Operad is an Automorphism

2025/11/06 by Rolf, Alice
#55P48 (Primary 18N70 #55R37 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2511.04828

Abstract

In a recent paper, Horel-Krannich-Kupers proved that all endomorphisms of the little d-disk operad are automorphisms. In this paper we show that this is also true for the framed little d-disk operad by using the classification of self maps of simple Lie groups. We also examine whether this property holds for the swiss cheese operad and prove that it holds for some other semidirect products of a group with a little disk operad.

Citations

• Mapping spaces of Swiss cheese operads
• Two remarks on spaces of maps between operads of little cubes
• Diffeomorphisms of discs and the second Weiss derivative of BTop(-)
• Delooping the functor calculus tower
• Profinite completion of operads and the Grothendieck-Teichmüller group
• Higher Topos Theory
• The Swiss-Cheese Operad

Related

• Automorphisms of framed operads
• Automorphisms of the little disks operad with torsion coefficients
• Profinite completion of operads and the Grothendieck-Teichmüller group
• Two remarks on spaces of maps between operads of little cubes
• Canonical extension of endomorphisms of type III factors