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DR/DZ equivalence
conjecture and tautological relations
Alexandr Buryak, Jérémy Guéré and Paolo Rossi |
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Geometry & Topology 23 (2019) 3537–3600
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Abstract |
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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 and and also when first pushed forward from to and then restricted to for any . 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 . As an application we find a new formula for the class as a linear combination of dual trees intersected with kappa- and psi-classes, and we check it for . |
Keywords
moduli space of curves, cohomology, double ramification
cycle, partial differential equations
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Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 37K10
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References |
Publication
Received: 5 May 2018
Accepted: 4 November 2018
Published: 30 December 2019
Proposed: Yasha Eliashberg
Seconded: Richard Thomas, Jim Bryan
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Authors |
| Alexandr Buryak | |
| School of Mathematics University of Leeds Leeds United Kingdom |
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| https://sites.google.com/site/alexandrburyakhomepage/home | |
| Jérémy Guéré | |
| Université Grenoble Alpes CNRS Institut Fourier Grenoble France |
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| https://www-fourier.ujf-grenoble.fr/~guerej/index.html | |
| Paolo Rossi | |
| Dipartimento di Matematica “Tullio
Levi-Civita” Università degli Studi di Padova Padova Italy |
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| http://www.math.unipd.it/~rossip/ | |
