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Dedicated to the memory of Victor Petrovich Havin.Abstract. Let Ω ⊂ R 2 be a countably connected domain. To any closed differential form of degree 1 in Ω with components in L 2 (Ω) one associates the sequence of its periods around holes in Ω, that is around bounded connected components of R 2 \ Ω. For which Ω the collection of such period sequences coincides with 2 ? We give the answer in terms of metric properties of holes in Ω.

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