Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces
Yukio Matsumoto, José Mariá Montesinos-Amilibia
Abstract
We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem will give a complete set of conjugacy invariants for the mapping classes of such homeomorphisms. This latter result implies that Nielsen's set of invariants [ Surface transformation classes of algebraically finite type, Collected Papers 2, Birkhäuser (1986)] is not complete.
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