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

Volume 30
Issue 7, 2431–2778
Issue 6, 2043–2429
Issue 5, 1611–2042
Issue 4, 1203–1610
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
Quantum Steenrod operations of symplectic resolutions

Jae Hee Lee

Geometry & Topology 29 (2025) 4341–4387
Bibliography
1 M Abouzaid, M McLean, I Smith, Gromov–Witten invariants in complex and Morava-local K-theories, Geom. Funct. Anal. 34 (2024) 1647 MR4823210
2 C Allday, V Puppe, Cohomological methods in transformation groups, 32, Cambridge Univ. Press (1993) MR1236839
3 O Biquard, Sur les équations de Nahm et la structure de Poisson des algèbres de Lie semi-simples complexes, Math. Ann. 304 (1996) 253 MR1371766
4 A Braverman, D Maulik, A Okounkov, Quantum cohomology of the Springer resolution, Adv. Math. 227 (2011) 421 MR2782198
5 M Brion, Poincaré duality and equivariant (co)homology, Michigan Math. J. 48 (2000) 77 MR1786481
6 M Brion, Lectures on the geometry of flag varieties, from: "Topics in cohomological studies of algebraic varieties" (editor P Pragacz), Birkhäuser (2005) 33 MR2143072
7 E Çineli, V L Ginzburg, B Z Gürel, From pseudo-rotations to holomorphic curves via quantum Steenrod squares, Int. Math. Res. Not. 2022 (2022) 2274 MR4373235
8 N Chriss, V Ginzburg, Representation theory and complex geometry, Birkhäuser (1997) MR1433132
9 I Danilenko, Quantum cohomology of slices of the affine Grassmannian, PhD thesis, Columbia University (2020) MR4094304
10 V V Deodhar, On some geometric aspects of Bruhat orderings, I : A finer decomposition of Bruhat cells, Invent. Math. 79 (1985) 499 MR782232
11 P Etingof, A Varchenko, p-curvature of periodic pencils of flat connections, preprint (2024) arXiv:2401.05652
12 P Etingof, A Varchenko, Periodic and quasi-motivic pencils of flat connections, preprint (2024) arXiv:2401.00636
13 K Fukaya, Morse homotopy and its quantization, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2.1, Amer. Math. Soc. (1997) 409 MR1470740
14 E González, C Y Mak, D Pomerleano, Affine nil-Hecke algebras and quantum cohomology, Adv. Math. 415 (2023) 108867 MR4541338
15 H Iritani, Shift operators and toric mirror theorem, Geom. Topol. 21 (2017) 315 MR3608715
16 D Kaledin, Geometry and topology of symplectic resolutions, from: "Algebraic geometry, II" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 595 MR2483948
17 J Kamnitzer, M McBreen, N Proudfoot, The quantum Hikita conjecture, Adv. Math. 390 (2021) 107947 MR4295090
18 N M Katz, Nilpotent connections and the monodromy theorem : Applications of a result of Turrittin, Inst. Hautes Études Sci. Publ. Math. 39 (1970) 175 MR291177
19 N M Katz, Algebraic solutions of differential equations (p-curvature and the Hodge filtration), Invent. Math. 18 (1972) 1 MR337959
20 J H Lee, Flat endomorphisms for modp equivariant quantum connections from quantum Steenrod operations, Selecta Math. 31 (2025) 15 MR4848887
21 T Liebenschutz-Jones, An intertwining relation for equivariant Seidel maps, preprint (2020) arXiv:2010.03342
22 T Liebenschutz-Jones, Shift operators and connections on equivariant symplectic cohomology, preprint (2021) arXiv:2104.01891
23 G Lonergan, Steenrod operators, the Coulomb branch and the Frobenius twist, Compos. Math. 157 (2021) 2494 MR4334711
24 D Maulik, A Okounkov, Quantum groups and quantum cohomology, 408, Soc. Math. France (2019) MR3951025
25 D McDuff, D Salamon, J-holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2012) MR2954391
26 D McDuff, S Tolman, Topological properties of Hamiltonian circle actions, IMRP Int. Math. Res. Pap. (2006) 72826, 1 MR2210662
27 H Nakajima, Instantons on ALE spaces, quiver varieties, and Kac–Moody algebras, Duke Math. J. 76 (1994) 365 MR1302318
28 A Okounkov, Lectures on K-theoretic computations in enumerative geometry, from: "Geometry of moduli spaces and representation theory" (editors R Bezrukavnikov, A Braverman, Z Yun), IAS/Park City Math. Ser. 24, Amer. Math. Soc. (2017) 251 MR3752463
29 A Okounkov, R Pandharipande, Quantum cohomology of the Hilbert scheme of points in the plane, Invent. Math. 179 (2010) 523 MR2587340
30 A F Ritter, Floer theory for negative line bundles via Gromov–Witten invariants, Adv. Math. 262 (2014) 1035 MR3228449
31 A F Ritter, F Živanović, Filtrations on quantum cohomology from the Floer theory of -actions, preprint (2023) arXiv:2304.13026
32 V Schechtman, A Varchenko, Solutions of KZ differential equations modulo p, Ramanujan J. 48 (2019) 655 MR3928838
33 P Seidel, π1 of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal. 7 (1997) 1046 MR1487754
34 P Seidel, Formal groups and quantum cohomology, Geom. Topol. 27 (2023) 2937 MR4668093
35 P Seidel, I Smith, Localization for involutions in Floer cohomology, Geom. Funct. Anal. 20 (2010) 1464 MR2739000
36 P Seidel, N Wilkins, Covariant constancy of quantum Steenrod operations, J. Fixed Point Theory Appl. 24 (2022) 52 MR4440845
37 E Shelukhin, Pseudo-rotations and Steenrod squares revisited, Math. Res. Lett. 28 (2021) 1255 MR4344705
38 A Smirnov, A Varchenko, The p-adic approximations of vertex functions via 3D mirror symmetry, Lett. Math. Phys. 115 (2025) 56 MR4908958
39 C Su, Restriction formula for stable basis of the Springer resolution, Selecta Math. 23 (2017) 497 MR3595900
40 C Su, C Zhong, Stable bases of the Springer resolution and representation theory, from: "Schubert calculus and its applications in combinatorics and representation theory" (editors J Hu, C Li, L C Mihalcea), Springer Proc. Math. Stat. 332, Springer (2020) 195 MR4167517
41 A Varchenko, An invariant subbundle of the KZ connection mod p and reducibility of 𝔰l2 Verma modules mod p, Math. Notes 109 (2021) 386 MR4310731
42 A Varchenko, Dynamical and qKZ equations modulo ps : an example, Math. Notes 112 (2022) 1003 MR4529619
43 C Voisin, A mathematical proof of a formula of Aspinwall and Morrison, Compositio Math. 104 (1996) 135 MR1421397
44 C Wendl, Lectures on holomorphic curves in symplectic and contact geometry, preprint (2010) arXiv:1011.1690
45 N Wilkins, A construction of the quantum Steenrod squares and their algebraic relations, Geom. Topol. 24 (2020) 885 MR4153653