Every Endomorphism of the Framed Little Disk Operad is an Automorphism
Algebraic Topology
2025-11-10 v1 Geometric Topology
Abstract
In a recent paper, Horel-Krannich-Kupers proved that all endomorphisms of the little -disk operad are automorphisms. In this paper we show that this is also true for the framed little -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.
Cite
@article{arxiv.2511.04828,
title = {Every Endomorphism of the Framed Little Disk Operad is an Automorphism},
author = {Alice Rolf},
journal= {arXiv preprint arXiv:2511.04828},
year = {2025}
}