4,297 research outputs found
Self-intersection numbers of length-equivalent curves on surfaces
Two free homotopy classes of closed curves in an orientable surface with
negative Euler characteristic are said to be length equivalent if for any
hyperbolic structure on the surface, the length of the geodesic in one class is
equal to the length of the geodesic in the other class. We show that there are
elements in the free group of two generators that are length equivalent and
have different self-intersection numbers as elements in the fundamental group
of the punctured torus and as elements in the pair of pants. This result
answers open questions about length equivalence classes and raises new ones
Please, Miss Central, Find My Mamma
https://digitalcommons.library.umaine.edu/mmb-vp/2926/thumbnail.jp
- …