A quasiconformal mapping class group acting trivially on the asymptotic Teichmüller space

Matsuzaki, Katsuhiko

doi:10.1090/S0002-9939-07-08761-8

A quasiconformal mapping class group acting trivially on the asymptotic Teichmüller space
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Proc. Amer. Math. Soc. 135 (2007), 2573-2579 Request permission

Abstract:

For an analytically infinite Riemann surface $R$, the quasiconformal mapping class group $\operatorname {MCG}(R)$ always acts faithfully on the ordinary Teichmüller space $T(R)$. However in this paper, an example of $R$ is constructed for which $\operatorname {MCG}(R)$ acts trivially on its asymptotic Teichmüller space $AT(R)$.

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