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Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces

Yukio Matsumoto·José Mariá Montesinos-Amilibia
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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.

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Yukio Matsumoto, José Mariá Montesinos-Amilibia. 1994-01-01. Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces. https://arxiv.org/abs/math/9401223

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