The 1st a part of the booklet reports pseudo-periodic maps of a closed floor of genus more than or equivalent to 2. This category of homeomorphisms was once initially brought by way of J. Nielsen in 1944 as an extension of periodic maps. during this publication, the conjugacy periods of the (chiral) pseudo-periodic mapping sessions are thoroughly categorized, 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's proven that the set of topological varieties of the entire singular fibers showing in a single parameter holomorphic households of Riemann surfaces is in a bijective correspondence with the set of conjugacy periods of the pseudo-periodic maps of adverse twists. The correspondence is given through the topological monodromy.
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