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Periods of abelian differentials and dynamics

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Given a closed oriented surface S of genus ≥ 3 we describe those cohomology classes χ ∈ H1(S,C) which appear as the period characters of abelian differentials for some choice of complex structure τ = τ(χ) on S consistent with the orientation. In other words, we describe the union Uτ∈T(S) H1,0(S,ℂ), where T(S) is the Teichmüller space of S. The proof is based upon Ratners solution of Raghunathans conjecture.

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