On framed simple purely real Hurwitz numbers

We study real Hurwitz numbers enumerating real meromorphic functions of a special kind, referred to as framed purely real functions. We deduce partial differential equations of cut-and-join type for the generating functions for these numbers. We also construct a topological field theory for them.

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Bibliographic Details
Published in:Izvestiya. Mathematics 2021-08, Vol.85 (4), p.681-704
Main Authors: Kazarian, M. E., Lando, S. K., Natanzon, S. M.
Format: Article
Language:English
Subjects:
cut-and-join equation
Field theory
Meromorphic functions
Numbers
Partial differential equations
real algebraic curve
real meromorphic function
real simple Hurwitz number
simple Hurwitz number
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Description
Summary:We study real Hurwitz numbers enumerating real meromorphic functions of a special kind, referred to as framed purely real functions. We deduce partial differential equations of cut-and-join type for the generating functions for these numbers. We also construct a topological field theory for them.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM9022