Pseudo-periodic Maps and Degeneration of Riemann Surfaces

2011
ISBN: 978-3-642-22533-8
Verlag: Springer

Buch, Englisch, Band 2030, 240 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 394 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Montesinos-Amilibia, José María

Matsumoto, Yukio

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Part I: Conjugacy Classification of Pseudo-periodic Mapping Classes.- 1 Pseudo-periodic Maps.- 2 Standard Form.- 3 Generalized Quotient.- 4 Uniqueness of Minimal Quotient.- 5 A Theorem in Elementary Number Theory.- 6 Conjugacy Invariants.- Part II: The Topology of Degeneration of Riemann Surfaces.- 7 Topological Monodromy.- 8 Blowing Down Is a Topological Operation.- 9 Singular Open-Book.