Superinjective Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces

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We prove that each superinjective simplicial map of the complex of curves of a compact, connected, nonorientable surface is induced by a homeomorphism of the surface, if (g, n) ∈ {(1, 0), (1, 1), (2, 0), (2, 1), (3, 0)} or g + n ≥ 5, where g is the genus of the surface and n is the number of the boundary components.