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

Volume 30, 1 issue

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 $K$-invariants and Gopakumar–Vafa invarints, II: Calabi–Yau threefolds at genus zero

You-Cheng Chou and Yuan-Pin Lee

Geometry & Topology 29 (2025) 4665–4693
DOI: 10.2140/gt.2025.29.4665
Bibliography
1 A S Buch, L C Mihalcea, Quantum K-theory of Grassmannians, Duke Math. J. 156 (2011) 501 MR2772069
2 A S Buch, P E Chaput, L C Mihalcea, N Perrin, Finiteness of cominuscule quantum K-theory, Ann. Sci. Éc. Norm. Supér. 46 (2013) 477 MR3099983
3 A S Buch, S Chung, C Li, L C Mihalcea, Euler characteristics in the quantum K-theory of flag varieties, Selecta Math. 26 (2020) 29 MR4083680
4 Y C Chou, Integrality of genus zero Gopakumar–Vafa type invariants of semi-positive varieties, Internat. J. Modern Phys. A 39 (2024) 2446014 MR4850082
5 Y C Chou, Y P Lee, Gopakumar–Vafa Invariants = Quantum K-invariants on Calabi–Yau threefolds, preprint (2022) arXiv:2212.13432
6 Y C Chou, Y P Lee, Quantum K-invariants and Gopakumar–Vafa invariants, I : The quintic threefold, preprint (2022) arXiv:2211.00788
7 D Edidin, Riemann–Roch for Deligne–Mumford stacks, from: "A celebration of algebraic geometry" (editors B Hassett, J McKernan, J Starr, R Vakil), Clay Math. Proc. 18, Amer. Math. Soc. (2013) 241 MR3114943
8 H Fan, Y P Lee, Towards a quantum Lefschetz hyperplane theorem in all genera, Geom. Topol. 23 (2019) 493 MR3921324
9 A Givental, On the WDVV equation in quantum K-theory, Michigan Math. J. 48 (2000) 295 MR1786492
10 A Givental, Permutation-equivariant quantum K-theory, II: Fixed point localization, preprint (2015) arXiv:1508.04374
11 A Givental, Permutation-equivariant quantum K-theory, III : Lefschetz’ formula on 0,n∕Sn and adelic characterization, preprint (2015) arXiv:1508.06697
12 A Givental, Permutation-equivariant quantum K-theory, IV : Dq-modules, preprint (2015) arXiv:1509.00830
13 A Givental, Permutation-equivariant quantum K-theory, V : Toric q-hypergeometric functions, preprint (2015) arXiv:1509.03903
14 A Givental, Permutation-equivariant quantum K-theory, VI: Mirrors, preprint (2015) arXiv:1509.07852
15 A Givental, Permutation-equivariant quantum K-theory, VII: General theory, preprint (2015) arXiv:1510.03076
16 A Givental, Permutation-equivariant quantum K-theory, VIII: Explicit reconstruction, preprint (2015) arXiv:1510.06116
17 A Givental, Explicit reconstruction in quantum cohomology and K-theory, Ann. Fac. Sci. Toulouse Math. 25 (2016) 419 MR3530164
18 A Givental, Permutation-equivariant quantum K-theory, I : Definitions : elementary K-theory of 0,n∕Sn, Mosc. Math. J. 17 (2017) 691 MR3734658
19 A Givental, Permutation-equivariant quantum K-theory, IX : Quantum Hirzebruch–Riemann–Roch in all genera, preprint (2017) arXiv:1709.03180
20 A Givental, Permutation-equivariant quantum K-theory, XI : Quantum Adams–Riemann–Roch, preprint (2017) arXiv:1711.04201
21 A Givental, Permutation-equivariant quantum K-theory, X : Quantum Hirzebruch–Riemann–Roch in genus 0, Symmetry Integrability Geom. Methods Appl. 16 (2020) 031 MR4089511
22 A Givental, Y P Lee, Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups, Invent. Math. 151 (2003) 193 MR1943747
23 E N Ionel, T H Parker, The Gopakumar–Vafa formula for symplectic manifolds, Ann. of Math. 187 (2018) 1 MR3739228
24 H Jockers, P Mayr, Quantum K-theory of Calabi–Yau manifolds, J. High Energy Phys. (2019) 011 MR4069552
25 H Jockers, P Mayr, A 3d gauge theory/quantum K-theory correspondence, Adv. Theor. Math. Phys. 24 (2020) 327 MR4125364
26 Y P Lee, Quantum K-theory, I : Foundations, Duke Math. J. 121 (2004) 389 MR2040281
27 D Maulik, Y Toda, Gopakumar–Vafa invariants via vanishing cycles, Invent. Math. 213 (2018) 1017 MR3842061
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 V Tonita, A virtual Kawasaki–Riemann–Roch formula, Pacific J. Math. 268 (2014) 249 MR3207609
30 C Voisin, A mathematical proof of a formula of Aspinwall and Morrison, Compositio Math. 104 (1996) 135 MR1421397