Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 349-363

TOPOLOGICAL CLASSIFICATION OF GENERIC REAL MEROMORPHIC FUNCTIONS FROM COMPACT SURFACES

Antonio F. Costa, Sergey Natanzon and Boris Shapiro

UNED, Facultad de Ciencias, Departamento de Matemáticas Fundamentales
C. Senda del rey, 9, 28040 Madrid, Spain; acosta 'at' mat.uned.es

National Research University Higher School of Economics (HSE)
20 Myasnitskaya ulitsa, Moscow 101000, Russia; natanzons 'at' mail.ru

Stockholm University, Department of Mathematics
SE-106 91 Stockholm, Sweden; shapiro 'at' math.su.se

Abstract. In this article, to each generic real meromorphic function (i.e., having only simple branch points in the appropriate sense) we associate a certain combinatorial gadget which we call the park of a function. We show that the park determines the topological type of the generic real meromorphic function and the set of parks produce a stratification of the space of generic real meromorphic functions. For any of the above topological types, we introduce and calculate the corresponding Hurwitz number. Finally we relate the topological types of generic real meromorphic functions with the monodromy of orbifold coverings.

2010 Mathematics Subject Classification: Primary 14P25; Secondary 14E22, 37F10.

Key words: Real meromorphic functions, gardens and parks, Hurwitz numbers.

Reference to this article: A. F. Costa, S. Natanzon and B. Shapiro: Topological classification of generic real meromorphic functions from compact surfaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 349-363.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4319