Pseudo-periodic Maps and Degeneration of Riemann Surfaces

  • Yukio Matsumoto
  • José María Montesinos-Amilibia

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Conjugacy Classification of Pseudo-periodic Mapping Classes

    1. Front Matter
      Pages 1-1
    2. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 3-15
    3. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 17-52
    4. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 53-92
    5. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 93-129
    6. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 131-144
    7. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 145-169
  3. The Topology of Degeneration of Riemann Surfaces

    1. Front Matter
      Pages 171-171
    2. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 173-188
    3. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 189-198
    4. Yukio Matsumoto, José María Montesinos-Amilibia
      Pages 199-220
  4. Back Matter
    Pages 221-238

About this book

Introduction

The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Keywords

14-XX; 57-XX chorizo spaces degeneration of Riemann surface pseudo-periodic maps topological monodromy

Authors and affiliations

  • Yukio Matsumoto
    • 1
  • José María Montesinos-Amilibia
    • 2
  1. 1.Department of MathematicsGakushuin UniversityToshima-kuJapan
  2. 2.Facultad de Matemáticas, Departamento de Geometría y TopologíaUniversidad ComplutenseMadridSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22534-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-22533-8
  • Online ISBN 978-3-642-22534-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book