Donaldson-Thomas theory and cluster algebras

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.

39 pages, 8 figures, mostly rewritten

References in corpus (2)

• Quiver varieties and cluster algebras
• Non-commutative Donaldson-Thomas theory and the conifold

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• Donaldson-Thomas invariants from tropical disks
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