#### Volume 19, issue 5 (2015)

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Motivic Donaldson–Thomas invariants for the one-loop quiver with potential

### Ben Davison and Sven Meinhardt

Geometry & Topology 19 (2015) 2535–2555
##### Abstract

We compute the motivic Donaldson–Thomas invariants of the one-loop quiver, with an arbitrary potential. This is the first computation of motivic Donaldson–Thomas invariants to use in an essential way the full machinery of $\stackrel{̂}{\mu }$–equivariant motives, for which we prove a dimensional reduction result similar to that of Behrend, Bryan and Szendrői in their study of degree-zero motivic Donaldson–Thomas invariants. Our result differs from theirs in that it involves nontrivial monodromy.

##### Keywords
motivic Donaldson–Thomas theory, vanishing cycles, quivers
Primary: 14N35
Secondary: 14D23