## Geometry & Topology

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

#### 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 $μ̂$–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.

#### Article information

Source
Geom. Topol., Volume 19, Number 5 (2015), 2535-2555.

Dates
Revised: 26 August 2014
Accepted: 30 September 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858844

Digital Object Identifier
doi:10.2140/gt.2015.19.2535

Mathematical Reviews number (MathSciNet)
MR3416109

Zentralblatt MATH identifier
06503548

#### Citation

Davison, Ben; Meinhardt, Sven. Motivic Donaldson–Thomas invariants for the one-loop quiver with potential. Geom. Topol. 19 (2015), no. 5, 2535--2555. doi:10.2140/gt.2015.19.2535. https://projecteuclid.org/euclid.gt/1510858844

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