All autoequivalences are spherical twists
Algebraic Geometry
2020-10-14 v3 Category Theory
Rings and Algebras
Abstract
In this short note we observe that, for purely formal reasons, any autoequivalence can be constructed as a twist around a spherical functor. As an example, we show how the P-twists constructed by Huybrechts and Thomas can be formulated as spherical twists.
Cite
@article{arxiv.1603.06717,
title = {All autoequivalences are spherical twists},
author = {Ed Segal},
journal= {arXiv preprint arXiv:1603.06717},
year = {2020}
}
Comments
11 pages at a relaxed pace. V2: Added funder acknowledgement. Published in IMRN. V3: `Proposition' 3.11 (which was only sketched) is wrong - added a counterexample due to Merlin Christ