Two transverse essential simple curves or proper arcs on a surface are in minimal position exactly when they form no bigon. For proper arcs, the proof uses the compactification of the universal cover to control their ends at punctures.

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  1. Minimal position of curves or arcs
  2. Essential proper arc on a punctured surface
  3. Mapping class group
  4. Topological surface
  5. Topology
  6. Geometry and topology
  7. Area of mathematics
  8. Mathematics
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