Donaldson-thomas theory and cluster Algebras

摘要

We provide a transformation formula of the (Euler characteristic version of the) noncommutative 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 provide alternative proofs of Fomin- Zelevinsky conjectures on cluster algebras.