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Conjugacy Invariants

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

Abstract

Let \( f:{\Sigma_g}\rightarrow{\Sigma_g}\) be a pseudo-periodic map of negative twist. According to Corollary 4.5, the isomorphism class of the minimal quotient \(\pi:{\Sigma_g}\rightarrow {S[f]}\) and, in particular, the numerical homeomorphism type of S[f] are conjugacy invariants of \( [f]\epsilon {\mathcal{M}_g}\). However, the converse is not true: the minimal quotient does not necessarily determine the conjugacy class of [f]. (Nielsen [50, Sect. 15] incorrectly claims that this converse is true (compare Theorem 13.4 of [22] where this same claim is repeated)).

Keywords

  • Conjugacy Class
  • Boundary Curve
  • Isomorphism Class
  • Boundary Component
  • Cohomology Class

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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). Conjugacy Invariants. 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_6

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