Geometry & Topology Volume 26, issue 4 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Procedure

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Other MSP Journals

The quantum Witten–Kontsevich series and one-part double Hurwitz numbers

Xavier Blot

Geometry & Topology 26 (2022) 1669–1743

DOI: 10.2140/gt.2022.26.1669

Bibliography

1	A Buryak, Double ramification cycles and integrable hierarchies, Comm. Math. Phys. 336 (2015) 1085 MR3324138
2	A Buryak, B Dubrovin, J Guéré, P Rossi, Tau-structure for the double ramification hierarchies, Comm. Math. Phys. 363 (2018) 191 MR3849988
3	A Buryak, B Dubrovin, J Guéré, P Rossi, Integrable systems of double ramification type, Int. Math. Res. Not. 2020 (2020) 10381 MR4190406
4	A Buryak, J Guéré, P Rossi, DR/DZ equivalence conjecture and tautological relations, Geom. Topol. 23 (2019) 3537 MR4059088
5	A Buryak, P Rossi, Double ramification cycles and quantum integrable systems, Lett. Math. Phys. 106 (2016) 289 MR3462029
6	A Buryak, S Shadrin, L Spitz, D Zvonkine, Integrals of ψ–classes over double ramification cycles, Amer. J. Math. 137 (2015) 699 MR3357119
7	B Dubrovin, Y Zhang, Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov–Witten invariants, preprint (2001) arXiv:math/0108160
8	T Ekedahl, S Lando, M Shapiro, A Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves, Invent. Math. 146 (2001) 297 MR1864018
9	C Faber, R Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. 7 (2005) 13 MR2120989
10	C Faber, R Pandharipande, Tautological and non-tautological cohomology of the moduli space of curves, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International (2013) 293 MR3184167
11	C Faber, S Shadrin, D Zvonkine, Tautological relations and the r–spin Witten conjecture, Ann. Sci. École Norm. Sup. 43 (2010) 621 MR2722511
12	I P Goulden, D M Jackson, R Vakil, Towards the geometry of double Hurwitz numbers, Adv. Math. 198 (2005) 43 MR2183250
13	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
14	M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 MR1171758
15	A Okounkov, Toda equations for Hurwitz numbers, Math. Res. Lett. 7 (2000) 447 MR1783622
16	A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. 163 (2006) 517 MR2199225
17	T K Petersen, Eulerian numbers, Birkhäuser (2015) MR3408615
18	E Witten, Two-dimensional gravity and intersection theory on moduli space, from: "Surveys in differential geometry" (editors H B Lawson Jr., S T Yau), Lehigh Univ. (1991) 243 MR1144529
19	E Witten, Algebraic geometry associated with matrix models of two-dimensional gravity, from: "Topological methods in modern mathematics" (editors L R Goldberg, A V Phillips), Publish or Perish (1993) 235 MR1215968