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The combinatorial formula for open gravitational descendents

Ran J Tessler

Geometry & Topology 27 (2023) 2497–2648
Bibliography
1 A Alexandrov, Open intersection numbers, matrix models and MKP hierarchy, J. High Energy Phys. (2015) 042 MR3340741
2 A Alexandrov, A Buryak, R J Tessler, Refined open intersection numbers and the Kontsevich–Penner matrix model, J. High Energy Phys. (2017) 123 MR3650694
3 A Bawane, H Muraki, C Rim, Open KdV hierarchy and minimal gravity on disk, Phys. Lett. B 783 (2018) 183 MR3840816
4 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
5 A Buryak, Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary, Lett. Math. Phys. 105 (2015) 1427 MR3395226
6 A Buryak, Open intersection numbers and the wave function of the KdV hierarchy, Mosc. Math. J. 16 (2016) 27 MR3470575
7 A Buryak, E Clader, R J Tessler, Open r–spin theory, II : The analogue of Witten’s conjecture for r–spin disks, preprint (2018) arXiv:1809.02536
8 A Buryak, E Clader, R J Tessler, Open r–spin theory, I : Foundations, Int. Math. Res. Not. 2022 (2022) 10458 MR4458550
9 A Buryak, A Netser Zernik, R Pandharipande, R J Tessler, Stationary open ℂℙ1 descendent theory, II : The open GW/H correspondence, in preparation
10 A Buryak, R J Tessler, Matrix models and a proof of the open analog of Witten’s conjecture, Comm. Math. Phys. 353 (2017) 1299 MR3652492
11 A Buryak, A N Zernik, R Pandharipande, R J Tessler, Open ℂℙ1 descendent theory, I : The stationary sector, Adv. Math. 401 (2022) 108249 MR4387849
12 D Cimasoni, N Reshetikhin, Dimers on surface graphs and spin structures, I, Comm. Math. Phys. 275 (2007) 187 MR2335773
13 P Deligne, D Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 75 MR262240
14 R Dijkgraaf, H Verlinde, E Verlinde, Loop equations and Virasoro constraints in nonperturbative two-dimensional quantum gravity, Nuclear Phys. B 348 (1991) 435 MR1083914
15 R Dijkgraaf, E Witten, Developments in topological gravity, preprint (2018) arXiv:1804.03275
16 K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant for general symplectic manifolds, from: "The Arnoldfest" (editors E Bierstone, B Khesin, A Khovanskii, J E Marsden), Fields Inst. Commun. 24, Amer. Math. Soc. (1999) 173 MR1733575
17 J Harris, I Morrison, Moduli of curves, 187, Springer (1998) MR1631825
18 T J Jarvis, Geometry of the moduli of higher spin curves, Internat. J. Math. 11 (2000) 637 MR1780734
19 T J Jarvis, T Kimura, A Vaintrob, Moduli spaces of higher spin curves and integrable hierarchies, Compositio Math. 126 (2001) 157 MR1827643
20 D Johnson, Spin structures and quadratic forms on surfaces, J. London Math. Soc. 22 (1980) 365 MR588283
21 D Joyce, D–manifolds, d–orbifolds and derived differential geometry : a detailed summary, preprint (2012) arXiv:1208.4948
22 D Joyce, On manifolds with corners, from: "Advances in geometric analysis" (editors S Janeczko, J Li, D H Phong), Adv. Lect. Math. 21, International (2012) 225 MR3077259
23 P W Kasteleyn, Dimer statistics and phase transitions, J. Mathematical Phys. 4 (1963) 287 MR153427
24 S Katz, C C M Liu, Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc, from: "The interaction of finite-type and Gromov–Witten invariants" (editors D Auckly, J Bryan), Geom. Topol. Monogr. 8, Geom. Topol. Publ. (2006) 1 MR2402818
25 M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 MR1171758
26 G Kuperberg, An exploration of the permanent-determinant method, Electron. J. Combin. 5 (1998) 46 MR1663576
27 C C M Liu, Moduli of J–holomorphic curves with Lagrangian boundary conditions and open Gromov–Witten invariants for an S1–equivariant pair, J. Iran. Math. Soc. 1 (2020) 5 MR4528678
28 E Looijenga, Cellular decompositions of compactified moduli spaces of pointed curves, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 369 MR1363063
29 M Mirzakhani, Weil–Petersson volumes and intersection theory on the moduli space of curves, J. Amer. Math. Soc. 20 (2007) 1 MR2257394
30 A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz numbers, and matrix models, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 325 MR2483941
31 R Pandharipande, J P Solomon, R J Tessler, Intersection theory on moduli of disks, open KdV and Virasoro, preprint (2014) arXiv:1409.2191
32 B Safnuk, Combinatorial models for moduli spaces of open Riemann surfaces, preprint (2016) arXiv:1609.07226
33 B Safnuk, Topological recursion for open intersection numbers, Commun. Number Theory Phys. 10 (2016) 833 MR3636676
34 J P Solomon, R J Tessler, Graded spin surfaces and the open Arf invariant, in preparation
35 J P Solomon, R J Tessler, Intersection theory on the moduli space of graded Riemann surfaces with boundary, in preparation
36 J P Solomon, S B Tukachinsky, Differential forms on orbifolds with corners, preprint (2020) arXiv:2011.10030
37 K Strebel, Quadratic differentials, 5, Springer (1984) MR743423
38 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
39 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
40 A N Zernik, Equivariant open Gromov–Witten theory of ℝℙ2mℂℙ2m, preprint (2017) arXiv:1709.09483
41 A N Zernik, Moduli of open stable maps to a homogeneous space, preprint (2017) arXiv:1709.07402
42 D Zvonkine, Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture, preprint (2002) arXiv:math/0209071