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Standard Form

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2030)

Abstract

Given a pseudo-periodic map \( f :{\Sigma_g}\rightarrow{\Sigma_g} \) Nielsen constructed a special homeomorphism which is homotopic to f and plays the role of a “standard form” in the mapping class of f , [53, Sect. 14]. In this Chapter, we will construct a similar standard form, slightly different from Nielsen’s, and will show its essential uniqueness. He wanted to avoid fixed points which might appear in annular neighborhoods of cut curves, while we do not care about such fixed points (Compare [22, Theorem 13.3]).

Keywords

  • Disjoint Union
  • Boundary Component
  • Dehn Twist
  • Small Positive Integer
  • Cyclic Orbit

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Correspondence to Yukio Matsumoto .

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© 2011 Springer-Verlag Berlin Heidelberg

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Matsumoto, Y., Montesinos-Amilibia, J.M. (2011). Standard Form. In: Pseudo-periodic Maps and Degeneration of Riemann Surfaces. Lecture Notes in Mathematics(), vol 2030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22534-5_2

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