Geometry & Topology Volume 23, issue 7 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

DOI: 10.2140/gt.2019.23.3537

Bibliography

1	A Buryak, Double ramification cycles and integrable hierarchies, Comm. Math. Phys. 336 (2015) 1085 MR3324138
2	A Y Buryak, New approaches to hierarchies of topological type, Uspekhi Mat. Nauk 72 (2017) 63 MR3716513
3	A Buryak, B Dubrovin, J Guéré, P Rossi, Tau-structure for the double ramification hierarchies, Comm. Math. Phys. 363 (2018) 191 MR3849988
4	A Buryak, B Dubrovin, J Guéré, P Rossi, Integrable systems of double ramification type, Int. Math. Res. Notices (2019)
5	A Buryak, J Guéré, Towards a description of the double ramification hierarchy for Witten’s r–spin class, J. Math. Pures Appl. 106 (2016) 837 MR3550848
6	A Buryak, H Posthuma, S Shadrin, A polynomial bracket for the Dubrovin–Zhang hierarchies, J. Differential Geom. 92 (2012) 153 MR2998900
7	A Buryak, P Rossi, Double ramification cycles and quantum integrable systems, Lett. Math. Phys. 106 (2016) 289 MR3462029
8	A Buryak, P Rossi, Recursion relations for double ramification hierarchies, Comm. Math. Phys. 342 (2016) 533 MR3459159
9	A Buryak, S Shadrin, L Spitz, D Zvonkine, Integrals of ψ–classes over double ramification cycles, Amer. J. Math. 137 (2015) 699 MR3357119
10	B Dubrovin, Y Zhang, Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov–Witten invariants, preprint (2001) arXiv:math/0108160
11	C Faber, Chow rings of moduli spaces of curves, I : The Chow ring of ℳ₃, Ann. of Math. 132 (1990) 331 MR1070600
12	C Faber, R Pandharipande, Hodge integrals and Gromov–Witten theory, Invent. Math. 139 (2000) 173 MR1728879
13	C Faber, R Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. 7 (2005) 13 MR2120989
14	E Getzler, Intersection theory on ℳ_1,4 and elliptic Gromov–Witten invariants, J. Amer. Math. Soc. 10 (1997) 973 MR1451505
15	E Getzler, Topological recursion relations in genus 2, from: "Integrable systems and algebraic geometry" (editors M H Saito, Y Shimizu, K Ueno), World Sci. (1998) 73 MR1672112
16	R Hain, Normal functions and the geometry of moduli spaces of curves, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International (2013) 527 MR3184171
17	E N Ionel, Topological recursive relations in H^2g(ℳ_g,n), Invent. Math. 148 (2002) 627 MR1908062
18	F Janda, Relations on M_g,n via equivariant Gromov–Witten theory of ℙ¹, preprint (2015) arXiv:1509.08421
19	F Janda, R Pandharipande, A Pixton, D Zvonkine, Double ramification cycles on the moduli spaces of curves, Publ. Math. Inst. Hautes Études Sci. 125 (2017) 221 MR3668650
20	M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
21	S Marcus, J Wise, Stable maps to rational curves and the relative Jacobian, preprint (2013) arXiv:1310.5981
22	R Pandharipande, A Pixton, D Zvonkine, Relations on ℳ_g,n via 3–spin structures, J. Amer. Math. Soc. 28 (2015) 279 MR3264769
23	P Rossi, Integrability, quantization and moduli spaces of curves, Symmetry Integrability Geom. Methods Appl. 13 (2017) MR3680568