Since fedja's excellent comment on Joseph's question on [probing a manifold with geodesics][1] remained uncommented (especially by topologists), I'd like to make a question out of it:

> **Conjecture:** Given an orientable 2-dimensional manifold and two
> closed curves on it which [intersect
> transversally][2] in exactly one
> point. Then the two curves cannot be
> homotopic.

(An immediate consequence of this would be that living on a surface with two such curves, one would know, that it is not homeomorphic to the sphere.)

> How to proof this conjecture (if it's true)? 


  [1]: https://mathoverflow.net/questions/81622/probing-a-manifold-with-geodesics
  [2]: http://mathworld.wolfram.com/TransversalIntersection.html