Volume 26, issue 2 (2022)

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Deformed dimensional reduction

Ben Davison and Tudor Pădurariu

Geometry & Topology 26 (2022) 721–776

Since its first use by Behrend, Bryan, and Szendrői in the computation of motivic Donaldson–Thomas (DT) invariants of 𝔸3, dimensional reduction has proved to be a crucial tool in motivic and cohomological DT theory. Inspired by a conjecture of Cazzaniga, Morrison, Pym and Szendrői on motivic DT invariants, work of Dobrovolska, Ginzburg and Travkin on exponential sums, and work of Orlov and Hirano on equivalences of categories of singularities, we generalize the dimensional reduction theorem in motivic and cohomological DT theory and use it to prove versions of the Cazzaniga–Morrison–Pym–Szendrői conjecture in these settings.

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Donaldson–Thomas invariants, quivers with potential
Mathematical Subject Classification
Primary: 14N35
Secondary: 16T99
Received: 14 May 2020
Revised: 13 January 2021
Accepted: 11 March 2021
Published: 15 June 2022
Proposed: Jim Bryan
Seconded: Paul Seidel, Richard P Thomas
Ben Davison
School of Mathematics
University of Edinburgh
United Kingdom
Tudor Pădurariu
Department of Mathematics
Columbia University
New York, NY
United States