Reduced Bers boundaries of Teichmüller spaces

Abstract

We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space into a point. This reduced Bers boundary turns out to be independent of the basepoint, and the action of the mapping class group on the Teichmüller space extends continuously to this boundary. We show that every auto-homeomorphism on the reduced Bers boundary comes from an extended mapping class. We also give a way to determine the limit in the reduced Bers boundary up to some ambiguity for parabolic curves for a given sequence in the Teichmüller space, by generalising the Thurston compactification.

Ver 2: minor corrections

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