Lecture Notes in Mathematics

Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Authors: Matsumoto, Yukio, Montesinos-Amilibia, José María

  • The publication of the manuscript which has been circulated among specialists for 20 years
  • The first complete study of pseudo-periodic maps after J. Nielsen's original work
  • The first application of the pseudo-periodic maps to the topology of degeneration of Riemann surfaces
  • This book is self-contained and is readable by advanced students (master level)
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About this book

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.

Reviews

From the reviews:

“The present monograph consists of two parts. In the first part a class of pseudo-periodic maps resp. mapping classes of closed surfaces is studied and classified up to conjugation (those of ‘negative twist’). This is motivated also by the second part on the topology of degenerating families of Riemann surfaces over a disk … . exposition is self-contained, elementary and written with great care for details … this makes arguments and proofs quite long, but certainly easy and pleasant to read.” (Bruno Zimmermann, Zentralblatt MATH, Vol. 1239, 2012)

“Surface mapping classes of algebraically finite type were introduced by Nielsen in 1944. … Nielsen’s arguments are sometimes considered as too vague, and one of the main objects of this book is to make Nielsen’s assertions precise. … The results in this book are given with detailed proofs. The book is well written and it should be useful for low-dimensional topologists and algebraic geometers.” (Athanase Papadopoulos, Mathematical Reviews, Issue 2012 h)


Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-22534-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-22533-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Pseudo-periodic Maps and Degeneration of Riemann Surfaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2030
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-22534-5
DOI
10.1007/978-3-642-22534-5
Softcover ISBN
978-3-642-22533-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 240
Number of Illustrations and Tables
55 b/w illustrations
Topics