The 1st a part of the publication stories pseudo-periodic maps of a closed floor of genus more than or equivalent to 2. This category of homeomorphisms was once initially brought through J. Nielsen in 1944 as an extension of periodic maps. during this publication, the conjugacy periods of the (chiral) pseudo-periodic mapping periods are thoroughly categorised, and Nielsen's incomplete class 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 forms of all of the singular fibers showing in a single parameter holomorphic s of Riemann surfaces is in a bijective correspondence with the set of conjugacy periods of the pseudo-periodic maps of destructive twists. The correspondence is given via the topological monodromy.
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