Duke Mathematical Journal

Donaldson–Thomas theory and cluster algebras

Kentaro Nagao

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

Article information

Duke Math. J., Volume 162, Number 7 (2013), 1313-1367.

First available in Project Euclid: 10 May 2013

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Zentralblatt MATH identifier

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 13F60: Cluster algebras


Nagao, Kentaro. Donaldson–Thomas theory and cluster algebras. Duke Math. J. 162 (2013), no. 7, 1313--1367. doi:10.1215/00127094-2142753. https://projecteuclid.org/euclid.dmj/1368193654

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