Deformed dimensional reduction

Davison, Ben; Pădurariu, Tudor

doi:10.2140/gt.2022.26.721

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Deformed dimensional reduction

Ben Davison and Tudor Pădurariu

Geometry & Topology 26 (2022) 721–776

DOI: 10.2140/gt.2022.26.721

Abstract

Since its first use by Behrend, Bryan, and Szendrői in the computation of motivic Donaldson–Thomas (DT) invariants of $𝔸_{ℂ}^{3}$ , 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.

Keywords

Donaldson–Thomas invariants, quivers with potential

Mathematical Subject Classification

Primary: 14N35

Secondary: 16T99

References

Publication

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

Authors

Ben Davison
School of Mathematics University of Edinburgh Edinburgh United Kingdom

Tudor Pădurariu
Department of Mathematics Columbia University New York, NY United States

Volume 26, issue 2 (2022)