Pseudo-periodic Maps and Degeneration of Riemann Surfaces

• 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.

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)