Topological classification of generic real rational functions

Sergei Natanzon, Boris Shapiro, Alek Vainshtein

Research output: Contribution to journalArticlepeer-review


To any real rational function with generic ramification points we assign a combinatorial object, called a garden, which consists of a weighted labeled directed planar chord diagram and of a set of weighted rooted trees each corresponding to a face of the diagram. We prove that any garden corresponds to a generic real rational function, and that equivalent functions have equivalent gardens.

Original languageEnglish
Pages (from-to)1063-1075
Number of pages13
JournalJournal of Knot Theory and its Ramifications
Issue number7
StatePublished - Nov 2002

Bibliographical note

Funding Information:
Partly supported by the INTAS grant 00-0259 and by the RFFI grant 01-01-00739.

Funding Information:
The authors are sincerely grateful to the Max-Planck Mathematical Institute in Bonn for the financial support and excellent research atmosphere during the fall of 2000 when this project was started. The second author wants to acknowledge the hospitality of IHES, Paris in January 2001 during the final stage of preparation of the manuscript.


  • Generic ramification
  • Hurwitz numbers
  • Real rational functions
  • Topological invariants

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Topological classification of generic real rational functions'. Together they form a unique fingerprint.

Cite this