Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

ON BALANCED PLANAR GRAPHS, FOLLOWING W. THURSTON

Abstract : Let f : S 2 → S 2 be an orientation-preserving branched covering map of degree d ≥ 2, and let Σ be an oriented Jordan curve passing through the critical values of f . Then Γ := f −1 (Σ) is an oriented graph on the sphere. In a group email discussion in Fall 2010, W. Thurston introduced balanced planar graphs and showed that they combinatorially characterize all such Γ, where f has 2d−2 distinct critical values. We give a detailed account of this discussion, along with some examples and an appendix about Hurwitz numbers.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [8 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01117927
Contributor : Lei Tan <>
Submitted on : Wednesday, February 18, 2015 - 11:01:05 AM
Last modification on : Tuesday, December 8, 2020 - 9:38:06 AM
Long-term archiving on: : Sunday, April 16, 2017 - 9:54:58 AM

File

New-balanced-maps.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01117927, version 1

Collections

Citation

Sarah Koch, Tan Lei. ON BALANCED PLANAR GRAPHS, FOLLOWING W. THURSTON. 2015. ⟨hal-01117927⟩

Share

Metrics

Record views

164

Files downloads

104