A Runge Approximation Theorem for Pseudo-Holomorphic Maps

The Runge approximation theorem for holomorphic maps is a fundamental result in complex analysis, and, consequently, many works have been devoted to extend it to other spaces (e.g. maps between certain algebraic varieties or complex manifolds). This article presents such a result for pseudo-holomorphic maps from a compact Riemann surface to a compact almost-complex manifold M, given that the manifold M admits many pseudo-holomorphic maps from $${\\mathbb {C}{\\rm P}^1}$$ which can be thought of as local approximations of the Laurent expansion az +br 2/z. This result specializes to some compact algebraic varieties (e.g. rationally connected projective varieties). An application to Lefschetz fibrations is presented