Flexibility of Embeddings of a Closed Curve System on the Orientable Surface

It has been proved that in the orientable surface of genus g(g ≥ 2), the number of pairwise disjoint, noncontractible and pairwise nonhomotopic cycles is at most 3g − 3. In this paper we mainly investigate the structure of the system of 3g − 3 pairwise disjoint, non-contractible and pairwise nonhomotopic closed curves in Sg, and we obtain some topological results for such 3g − 3 curves in Sg