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

Volume 30
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Intersection theory on moduli of disks, open KdV and Virasoro

Rahul Pandharipande, Jake P Solomon and Ran J Tessler

Geometry & Topology 28 (2024) 2483–2567
Bibliography
1 L V Ahlfors, L Sario, Riemann surfaces, 26, Princeton Univ. Press (1960) MR0114911
2 A Alexandrov, A Buryak, R J Tessler, Refined open intersection numbers and the Kontsevich–Penner matrix model, J. High Energy Phys. 2017 (2017) 123 MR3650694
3 A Basalaev, A Buryak, Open WDVV equations and Virasoro constraints, Arnold Math. J. 5 (2019) 145 MR4031355
4 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
5 A Buryak, E Clader, R J Tessler, Open r–spin theory, II : The analogue of Witten’s conjecture for r–spin disks, (2018) arXiv:1809.02536
6 A Buryak, E Clader, R J Tessler, Open r–spin theory, I : Foundations, Int. Math. Res. Not. 2022 (2022) 10458 MR4458550
7 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
8 A Buryak, A N Zernik, R Pandharipande, R J Tessler, Open ℂℙ1 descendent theory, I : The stationary sector, Adv. Math. 401 (2022) 108249 MR4387849
9 X Chen, Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants, Geom. Funct. Anal. 32 (2022) 490 MR4431122
10 X Chen, A Zinger, WDVV-type relations for disk Gromov–Witten invariants in dimension 6, Math. Ann. 379 (2021) 1231 MR4238264
11 C H Cho, Counting real J–holomorphic discs and spheres in dimension four and six, J. Korean Math. Soc. 45 (2008) 1427 MR2439744
12 K Cieliebak, I Mundet i Riera, D A Salamon, Equivariant moduli problems, branched manifolds, and the Euler class, Topology 42 (2003) 641 MR1953244
13 P Deligne, D Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 75 MR0262240
14 R Dijkgraaf, E Witten, Developments in topological gravity, Int. J. Modern Phys. A 33 (2018) 1830029 MR3875934
15 Y Eliashberg, Symplectic field theory and its applications, from: "International Congress of Mathematicians, I" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2007) 217 MR2334192
16 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. GAFA 2000 special volume (2000) 560 MR1826267
17 O Fabert, Gravitational descendants in symplectic field theory, Comm. Math. Phys. 302 (2011) 113 MR2770011
18 O Fabert, P Rossi, String, dilaton, and divisor equation in symplectic field theory, Int. Math. Res. Not. 2011 (2011) 4384 MR2838044
19 O Fabert, P Rossi, Topological recursion relations in non-equivariant cylindrical contact homology, J. Symplectic Geom. 11 (2013) 405 MR3100800
20 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, I, 46.1, Amer. Math. Soc. (2009) MR2553465
21 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, II, 46.2, Amer. Math. Soc. (2009) MR2548482
22 P Georgieva, Open Gromov–Witten disk invariants in the presence of an anti-symplectic involution, Adv. Math. 301 (2016) 116 MR3539371
23 E Getzler, R Pandharipande, Virasoro constraints and the Chern classes of the Hodge bundle, Nuclear Phys. B 530 (1998) 701 MR1653492
24 P Giterman, J P Solomon, Descendent open Gromov–Witten invariants, in preparation
25 J Harris, I Morrison, Moduli of curves, 187, Springer (1998) MR1631825
26 M W Hirsch, Differential topology, 33, Springer (1976) MR448362
27 H Hofer, J P Solomon, Inductive extension of multisections, in preparation
28 H Hofer, K Wysocki, E Zehnder, Polyfold and Fredholm theory, 72, Springer (2021) MR4298268
29 A Horev, J P Solomon, The open Gromov–Witten–Welschinger theory of blowups of the projective plane, preprint (2012) arXiv:1210.4034
30 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
31 M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 MR1171758
32 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
33 M Mirzakhani, Weil–Petersson volumes and intersection theory on the moduli space of curves, J. Amer. Math. Soc. 20 (2007) 1 MR2257394
34 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
35 B Riemann, Theorie der Abel’schen Functionen, J. Reine Angew. Math. 54 (1857) 115 MR1579035
36 P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
37 J P Solomon, Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions, PhD thesis, Massachusetts Institute of Technology (2006) arXiv:math.SG/0606429 MR2717339
38 J P Solomon, A differential equation for the open Gromov–Witten potential, preprint (2007)
39 J P Solomon, R J Tessler, Intersection theory on the moduli space of graded Riemann surfaces with boundary, in preparation
40 J P Solomon, S B Tukachinsky, Point-like bounding chains in open Gromov–Witten theory, Geom. Funct. Anal. 31 (2021) 1245 MR4356703
41 J P Solomon, S B Tukachinsky, Relative quantum cohomology, J. Eur. Math. Soc. (JEMS) 26 (2024) 3497 MR4767498
42 R J Tessler, The combinatorial formula for open gravitational descendents, Geom. Topol. 27 (2023) 2497 MR4645483
43 J Y Welschinger, Invariants of real symplectic 4–manifolds and lower bounds in real enumerative geometry, Invent. Math. 162 (2005) 195 MR2198329
44 E Witten, Topological sigma models, Comm. Math. Phys. 118 (1988) 411 MR0958805
45 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
46 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
47 A N Zernik, Equivariant open Gromov–Witten theory of ℝℙ2mℂℙ2m, preprint (2017) arXiv:1709.09483
48 A N Zernik, Fixed-point localization for ℝℙ2m ℂℙ2m, preprint (2017) arXiv:1703.02950
49 A N Zernik, Moduli of open stable maps to a homogeneous space, preprint (2017) arXiv:1709.07402