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Simultaneous diophantine approximation with quadratic and linear forms
Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials
1. | IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France |
  For every connected component of each stratum of Abelian and quadratic differentials we construct an explicit representative which is a Jenkins–Strebel differential with a single cylinder. By an elementary variation of this construction we represent almost every Abelian (quadratic) differential in the corresponding connected component of the stratum as a polygon with identified pairs of edges, where combinatorics of identifications is explicitly described.
  Specifically, the combinatorics is expressed in terms of a generalized permutation. For any component of any stratum of Abelian and quadratic differentials we construct a generalized permutation in the corresponding extended Rauzy class.
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