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Unstable quasi-geodesics in Teichmüller space. (English) Zbl 0960.30033
Kra, Irwin (ed.) et al., In the tradition of Ahlfors and Bers. Proceedings of the first Ahlfors-Bers colloquium, State University of New York, Stony Brook, NY, USA, November 6-8, 1998. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 256, 239-241 (2000).
The authors construct examples of unstable quasi-geodesics in the Teichmüller space. They show that for any hyperbolic surface $$S$$ whose Teichmüller space $${\mathcal T}(S)$$ has dimension at least 4, there is a bi-finite quasi-geodesic $$L$$ in $${\mathcal T}(S)$$ such that
1. $$L$$ projects to a compact part of the moduli space $${\mathcal M}(S)$$, but
2. $$L$$ does not lie in a bounded neighbourhood of any geodesic.
They thus answer in the negative a question asked by M. Mitra.
For the entire collection see [Zbl 0941.00017].

##### MSC:
 30F60 Teichmüller theory for Riemann surfaces 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
##### Keywords:
stability; Teichmüller space; quasi-geodesic; geodesic