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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)
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.