Kentaro ITO

Schottky groups and Bers boundary of Teichmueller space


We will show that every Kleinian groups on a Bers boundary of the Teichm\"{u}ller space is an algebraic limit of a sequence of Schottky groups. To show this, we extend the action of the mapping class group on a Bers slice to that on a class of function groups whose invariant components are covering some fixed Riemann surface. An important observation is that the orbit of every maximal cusp is dense in a Bers boundary.

submission: June 25, 1999

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