Analytic and topological nets.(English)Zbl 07967016
Summary: We characterize which planar graphs arise as the pullback, under a rational map \(r\), of an analytic Jordan curve passing through the critical values of \(r\). We also prove that such pullbacks are dense within the collection of \(f^{-1}(\Sigma)\), where \(f\) is a branched cover of the sphere and \(\Sigma\) is a Jordan curve passing through the branched values of \(f\).
MSC:
| 30C10 | Polynomials and rational functions of one complex variable |
| 30C62 | Quasiconformal mappings in the complex plane |
| 30E10 | Approximation in the complex plane |
| 41A20 | Approximation by rational functions |
Cite
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