TOPOLOGICAL CLASSIFICATION OF GENERIC REAL RATIONAL FUNCTIONS

@article{Natanzon2001TOPOLOGICALCO,
  title={TOPOLOGICAL CLASSIFICATION OF GENERIC REAL RATIONAL FUNCTIONS},
  author={S. Natanzon and B. Shapiro and A. Vainshtein},
  journal={Journal of Knot Theory and Its Ramifications},
  year={2001},
  volume={11},
  pages={1063-1075}
}
  • S. Natanzon, B. Shapiro, A. Vainshtein
  • Published 2001
  • Mathematics
  • Journal of Knot Theory and Its Ramifications
  • 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. 

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