During a generic isotopy of one transverse curve, crossings with a fixed curve can only be created or removed in pairs of opposite local sign. Their signed sum, and hence the algebraic intersection number, is therefore invariant.

Ancestors (9)

  1. Algebraic intersection number of curves on an oriented surface
  2. Geometric intersection number
  3. Mapping class group
  4. Topological surface
  5. Topology
  6. Geometry and topology
  7. Area of mathematics
  8. Mathematics
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