Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces

Matsumoto, Yukio; Montesinos-Amilibia, José María

doi:10.1090/S0273-0979-1994-00437-9

Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces

Authors: Yukio Matsumoto and José María Montesinos-Amilibia
Journal: Bull. Amer. Math. Soc. 30 (1994), 70-75
MSC (2000): Primary 30F60; Secondary 32G15, 57M99
DOI: https://doi.org/10.1090/S0273-0979-1994-00437-9
MathSciNet review: 1217354
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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 [Surface transformation classes of algebraically finite type, Collected Papers 2, Birkhäuser (1986)] is not complete.

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