Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces

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 [{\it Surface transformation classes of algebraically finite type}, Collected Papers 2, Birkh\"auser (1986)] is not complete.