Let P be a closed triangulated manifold, dimP=n. We consider the group of simplicial 1-chains C1(P)= C1(P,Z2) and the homology group H1(P)= H1(P,Z2). We also use some nonnegative weighting function L:C1(P)→R. For any homological class [x] ∈ H1(P) the method proposed in article builds a cycle z∈[x] with minimal weight L(z). The main idea is in using a simplicial scheme of space of the regular covering p: P' → P with automorphism group G ≅ H1(P). We construct this covering applying the index vector-function J:C1(P)→Z2r relative to any basis of group Hn-1(P), r= rank Hn-1(P).
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