Topological Monodromy

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


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 \({M^*}-{\psi^{-1}}(0)\).


Riemann Surface Conjugacy Class Disjoint Union Irreducible Component Mapping Class Group 
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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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