Volume 23, issue 7 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
DR/DZ equivalence conjecture and tautological relations

Alexandr Buryak, Jérémy Guéré and Paolo Rossi

Geometry & Topology 23 (2019) 3537–3600

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 ̄g,n+m to ̄g,n and then restricted to g,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.

moduli space of curves, cohomology, double ramification cycle, partial differential equations
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 37K10
Received: 5 May 2018
Accepted: 4 November 2018
Published: 30 December 2019
Proposed: Yasha Eliashberg
Seconded: Richard Thomas, Jim Bryan
Alexandr Buryak
School of Mathematics
University of Leeds
United Kingdom
Jérémy Guéré
Université Grenoble Alpes
Institut Fourier
Paolo Rossi
Dipartimento di Matematica “Tullio Levi-Civita”
Università degli Studi di Padova