Donaldson-Thomas theory and cluster algebras

TL;DR

This paper establishes a transformation formula for non-commutative Donaldson-Thomas invariants under mutations, linking cluster transformations with quiver Grassmannians and providing proofs for conjectures on $F$-polynomials and $g$-vectors.

Contribution

It introduces a new transformation formula for invariants under mutations and connects cluster algebra transformations with quiver Grassmannians, offering alternative proofs for key conjectures.

Findings

Transformation formula for non-commutative Donaldson-Thomas invariants

Description of cluster transformations via quiver Grassmannians

Proof of Fomin-Zelevinsky's conjectures on $F$-polynomials and $g$-vectors

Abstract

We provide a transformation formula of non-commutative Donaldson-Thomas invariants under a composition of mutations. Consequently, we get a description of a composition of cluster transformations in terms of quiver Grassmannians. As an application, we give an alternative proof of Fomin-Zelevinsky's conjectures on $F$-polynomials and $g$-vectors.