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Topological Monodromy

  • Yukio MatsumotoEmail author
  • José María Montesinos-Amilibia
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2030)

Abstract

A triple (M,D,ψ) is called a degenerating family of Riemann surfaces of genus g (abbreviated as degenerating family of genus g) if M is a complex surface, \( D=\{\xi \in \mathbf{C}||\xi|<1\},\)\(\psi:M\rightarrow D\) is a surjective proper holomorphic map, for each \(\psi:M\rightarrow D \), the fiber \( {F _\xi}={\psi^{-1}\Psi}(\xi)\) is connected, and \(\psi{|_{M^*}}:{M^*}\rightarrow {D^*}\) is a smooth (i.e.C) fiber bundle whose fiber is a Riemann surface of genus g, where \({D^*}=D-\{0\}\Psi\) and \({M^*}-{\psi^{-1}}(0)\).

Keywords

Riemann Surface Conjugacy Class Disjoint Union Irreducible Component Mapping Class Group 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yukio Matsumoto
    • 1
    Email author
  • José María Montesinos-Amilibia
    • 2
  1. 1.Department of MathematicsGakushuin UniversityTokyoJapan
  2. 2.Facultad de Matemáticas Departamento de Geometría y TopologíaUniversidad ComplutenseMadridSpain

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