Generalized Quotient

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


A periodic map f on a surface defines a quotient space ∑/f . In the case of a pseudo-periodic map \( f:{\Sigma}\rightarrow {\Sigma},\) however, the quotient space ∑/f would not be any reasonable space, if the term “quotient space” is taken in the usual sense, i.e., the orbit space under the action of f . To adjust this, we introduce the following definition.


Disjoint Union Irreducible Component Quotient Space Cyclic Covering Sphere Component 
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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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