Buryak, A, Guéré, J and Rossi, P (2019) DR/DZ equivalence conjecture and tautological relations. Geometry & Topology, 23 (7). pp. 3537-3600. ISSN 1465-3060
Abstract
We present a family of conjectural relations in the tautological ring of the moduli spaces of stable curves which implies the strong double ramification/Dubrovin–Zhang equivalence conjecture introduced by the authors with Dubrovin (Comm. Math. Phys. 363 (2018) 191–260). Our tautological relations have the form of an equality between two different families of tautological classes, only one of which involves the double ramification cycle. We prove that both families behave the same way upon pullback and pushforward with respect to forgetting a marked point. We also prove that our conjectural relations are true in genus 0 and 1 and also when first pushed forward from ˉMg,n+m to ˉMg,n and then restricted to Mg,n for any g,n,m≥0. Finally we show that, for semisimple CohFTs, the DR/DZ equivalence only depends on a subset of our relations, finite in each genus, which we prove for g≤2. As an application we find a new formula for the class λg as a linear combination of dual trees intersected with kappa- and psi-classes, and we check it for g≤3.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article is protected by copyright. This is an author produced version of a paper published in Geometry and Topology. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | moduli space of curves, cohomology, double ramification cycle, partial differential equations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Nov 2018 12:09 |
Last Modified: | 08 Jan 2020 20:41 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers |
Identification Number: | 10.2140/gt.2019.23.3537 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139359 |