The 1st a part of the e-book reviews pseudo-periodic maps of a closed floor of genus more than or equivalent to 2. This type of homeomorphisms was once initially brought by way of J. Nielsen in 1944 as an extension of periodic maps. during this e-book, the conjugacy periods of the (chiral) pseudo-periodic mapping sessions are thoroughly labeled, and Nielsen's incomplete type is corrected. the second one half applies the result of the 1st half to the topology of degeneration of Riemann surfaces. it truly is proven that the set of topological varieties of all of the singular fibers showing in a single parameter holomorphic households of Riemann surfaces is in a bijective correspondence with the set of conjugacy sessions of the pseudo-periodic maps of damaging twists. The correspondence is given by way of the topological monodromy.

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