Homotopical rigidity of the pre-Lie operad
K-Theory and Homology
2021-04-02 v2 Category Theory
Abstract
We show that the celebrated operad of pre-Lie algebras is very rigid: it has no "non-obvious" degrees of freedom from either of the three points of view: deformations of maps to and from the "three graces of operad theory", homotopy automorphisms, and operadic twisting. Examining the latter, it is possible to answer two questions of Markl from 2005, including a Lie-theoretic version of the Deligne conjecture.
Keywords
Cite
@article{arxiv.2002.12918,
title = {Homotopical rigidity of the pre-Lie operad},
author = {Vladimir Dotsenko and Anton Khoroshkin},
journal= {arXiv preprint arXiv:2002.12918},
year = {2021}
}
Comments
15 pages, final version, to appear in Proceedings of the AMS