A note on Gunningham’s formula. (English) Zbl 1471.14115
In this article, the author, using a gluing theorem for spin Hurwitz numbers, re-proves Gunningham’s formula which gives a closed formula for all spin Hurwitz numbers. The author also extends gluing theorem to include some additional cases for which spin Hurwitz numbers are not defined.
Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale)
MSC:
| 14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
| 81T45 | Topological field theories in quantum mechanics |
References:
| [1] | Abrams, L., Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory Ramifications, 5, 5, 569-587, (1996) · Zbl 0897.57015 · doi:10.1142/S0218216596000333 |
| [2] | Bryan, J.; Pandharipande, R., Curves in Calabi-Yau threefolds and topological quantum field theory, Duke Math. J., 126, 2, 369-396, (2005) · Zbl 1084.14053 · doi:10.1215/S0012-7094-04-12626-0 |
| [3] | Bryan, J.; Pandharipande, R., The local Gromov-Witten theory of curves. With an appendix by Bryan, C. Faber, A. Okounkov and Pandharipande, J. Amer. Math. Soc., 21, 1, 101-136, (2008) · Zbl 1126.14062 · doi:10.1090/S0894-0347-06-00545-5 |
| [4] | Cheng, S.-J.; Wang, W., Dualities and Representations of Lie Superalgebras, 144, (2012), American Mathematical Society: American Mathematical Society, Providence, RI · Zbl 1271.17001 · doi:10.1090/gsm/144 |
| [5] | Eskin, A.; Okounkov, A.; Pandharipande, R., The theta characteristic of a branched covering, Adv. Math., 217, 3, 873-888, (2008) · Zbl 1157.14014 · doi:10.1016/j.aim.2006.08.001 |
| [6] | Gunningham, S., Spin Hurwitz numbers and topological quantum field theory, Geom. Topol., 20, 4, 1859-1907, (2016) · Zbl 1347.81070 · doi:10.2140/gt.2016.20.1859 |
| [7] | Józefiak, T., Semisimple superalgebras, Algebra. Some Current Trends (Varna 1986), 1352, 96-113, (1988), Springer: Springer, Berlin · Zbl 0666.17001 · doi:10.1007/BFb0082020 |
| [8] | Józefiak, T., A Class of Projective Representations of Hyperoctahedral Groups and Schur Q-Functions, (1990), PWN-Polish Scientific Publishers: PWN-Polish Scientific Publishers, Warsaw · Zbl 0763.20006 |
| [9] | Joachim, K., Frobenius Algebras and 2D Topological Quantum Field Theories, 59, (2004), Cambridge University Press: Cambridge University Press, Cambridge · Zbl 1046.57001 |
| [10] | Kiem, Y.-H.; Li, J., Low degree GW invariants of spin surfaces, Pure Appl. Math. Q., 7, 4, 1449-1476, (2011) · Zbl 1328.14086 · doi:10.4310/PAMQ.2011.v7.n4.a17 |
| [11] | Lee, J.; Parker, T. H., A structure theorem for the Gromov-Witten invariants of Kähler Surfaces, J. Differential Geom., 77, 3, 483-513, (2007) · Zbl 1130.53059 · doi:10.4310/jdg/1193074902 |
| [12] | Lee, J.; Parker, T. H., Spin Hurwitz numbers and the Gromov-Witten invariants of Kahler surfaces, Comm. Anal. Geom., 21, 5, 1015-1060, (2013) · Zbl 1295.14050 · doi:10.4310/CAG.2013.v21.n5.a6 |
| [13] | Maulik, D.; Pandharipande, R., New calculations in Gromov-Witten theory, Pure Appl. Math. Q., 4, 2-1, 469-500, (2008) · Zbl 1156.14042 |
| [14] | Sergeev, A. N., Tensor algebra of the identity representation as a module over the Lie superalgebras Gl (n, m) and Q (n), Math. USSR Sbornik., 51, 1985, 419-425 · Zbl 0573.17002 · doi:10.1070/SM1985v051n02ABEH002867 |
| [15] | Serre, J.-P., Topics in Galois Theory, (1992), Jones and Bartlett: Jones and Bartlett, Boston · Zbl 0746.12001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
