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Pseudo-periodic Maps and Degeneration of Riemann Surfaces (Paperback, Edition.)
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Pseudo-periodic Maps and Degeneration of Riemann Surfaces (Paperback, Edition.)
Series: Lecture Notes in Mathematics, 2030
Expected to ship within 10 - 15 working days
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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.
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