Duke Mathematical Journal

Donaldson–Thomas theory and cluster algebras

Kentaro Nagao

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Abstract

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

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

Dates
First available in Project Euclid: 10 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1368193654

Digital Object Identifier
doi:10.1215/00127094-2142753

Mathematical Reviews number (MathSciNet)
MR3079250

Zentralblatt MATH identifier
1375.14150

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

Citation

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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