Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces
Complex Variables
2016-09-06 v1
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.
Keywords
Cite
@article{arxiv.math/9401223,
title = {Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces},
author = {Yukio Matsumoto and José Mariá Montesinos-Amilibia},
journal= {arXiv preprint arXiv:math/9401223},
year = {2016}
}
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6 pages