Topological classification of generic real rational functions

Details Topological classification of generic real rational functions Topological classification of generic real rational functions

2001-10-21

arxiv.org/abs/math/0110235v1

Mathematics

Algebraic Geometry

submitted to J. Knots Theory Ramifications

Scientific paper

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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