All autoequivalences are spherical twists

TL;DR

This paper demonstrates that all autoequivalences in a certain mathematical setting can be expressed as spherical twists, unifying various known autoequivalences under a common framework.

Contribution

It shows that any autoequivalence can be realized as a spherical twist, providing a formal and conceptual unification of autoequivalence constructions.

Findings

Any autoequivalence can be constructed as a spherical twist.

P-twists by Huybrechts and Thomas are examples of spherical twists.

The approach is purely formal, not relying on specific geometric data.

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.