On framed simple purely real Hurwitz numbers
- Authors: Kazarian M.E.1,2, Lando S.K.1,2, Natanzon S.M.1,3
-
Affiliations:
- HSE University
- Skolkovo Institute of Science and Technology
- State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics
- Issue: Vol 85, No 4 (2021)
- Pages: 69-95
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133849
- DOI: https://doi.org/10.4213/im9022
- ID: 133849
Cite item
Open Access
Access granted
Subscription Access
Abstract
We study real Hurwitz numbers enumerating real meromorphic functions of a special kind, referred to asframed purely real functions. We deduce partial differential equations of cut-and-join type for the generatingfunctions for these numbers. We also construct a topological field theory for them.
About the authors
Maxim Eduardovich Kazarian
HSE University; Skolkovo Institute of Science and Technology
Email: kazarian@mccme.ru
Doctor of physico-mathematical sciences, no status
Sergei Konstantinovich Lando
HSE University; Skolkovo Institute of Science and Technology
Email: lando@mccme.ru
Doctor of physico-mathematical sciences
Sergey Mironovich Natanzon
HSE University; State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics
Email: natanzon@mccme.ru
Doctor of physico-mathematical sciences, no status
References
- С. М. Натанзон, “Конечные группы гомеоморфизмов поверхностей и вещественные формы комплексных алгебраических кривых”, Тр. ММО, 51, Изд-во Моск. ун-та, М., 1988, 3–53
- S. M. Gusein-Zade, S. M. Natanzon, “Klein foams as families of real forms of Riemann surfaces”, Adv. Theor. Math. Phys., 21:1 (2017), 231–241
- I. P. Goulden, D. M. Jackson, “Transitive factorisations into transpositions and holomorphic mappings on the sphere”, Proc. Amer. Math. Soc., 125:1 (1997), 51–60
- С. М. Натанзон, “Дисковые одинарные числа Гурвица”, Функц. анализ и его прил., 44:1 (2010), 44–58
- I. Itenberg, D. Zvonkine, “Hurwitz numbers for real polynomials”, Comment. Math. Helv., 93:3 (2018), 441–474
- V. Arnold, “Topological classification of real trigonometric polynomials and cyclic serpents polyhedron”, The Arnold–Gelfand mathematical seminars, Birkhäuser Boston, Boston, MA, 1997, 101–106
- Б. З. Шапиро, “О числе компонент пространства тригонометрических многочленов степени $n$ с $2n$ различными критическими значениями”, Матем. заметки, 62:4 (1997), 635–640
- B. Z. Shapiro, A. D. Vainshtein, “Counting real rational functions with all real critical values”, Mosc. Math. J., 3:2 (2003), 647–659
- S. Natanzon, B. Shapiro, A. Vainshtein, “Topological classification of generic real rational functions”, J. Knot Theory Ramifications, 11:7 (2002), 1063–1075
- A. F. Costa, S. Natanzon, B. Shapiro, “Topological classification of generic real meromorphic functions from compact surfaces”, Ann. Acad. Sci. Fenn. Math., 43:1 (2018), 349–363
- С. А. Баранников, “О пространстве вещественных многочленов без кратных критических значений”, Функц. анализ и его прил., 26:2 (1992), 10–17
- R. Dijkgraaf, “Mirror symmetry and elliptic curves”, The moduli spaces of curves (Texel Island, 1994), Progr. Math., 129, Birkhäuser Boston, Boston, MA, 1995, 149–163
- A. Alexeevski, S. Natanzon, “Noncommutative two-dimensional topological field theories and Hurwitz numbers for real algebraic curves”, Selecta Math. (N.S.), 12:3-4 (2006), 307–377
- А. В. Алексеевский, С. М. Натанзон, “Алгебра двудольных графов и числа Гурвица лоскутных поверхностей”, Изв. РАН. Сер. матем., 72:4 (2008), 3–24
- A. V. Alexeevski, S. M. Natanzon, “Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy–Frobenius algebras of finite groups”, Geometry, topology, and mathematical physics, Amer. Math. Soc. Transl. Ser. 2, 224, Adv. Math. Sci., 61, Amer. Math. Soc., Providence, RI, 2008, 1–25
- A. Mironov, A. Morozov, S. Natanzon, “Cardy–Frobenius extension of the algebra of cut-and-join operators”, J. Geom. Phys., 73 (2013), 243–251
- A. Mironov, A. Morozov, S. Natanzon, “A Hurwitz theory avatar of open–closed strings”, Eur. Phys. J. C Part. Fields, 73:2 (2013), 2324, 10 pp.
- A. Mironov, A. Morozov, S. Natanzon, “Infinite-dimensional topological field theories from Hurwitz numbers”, J. Knot Theory Ramifications, 23:6 (2014), 1450033, 16 pp.
