Configuration Space Models for Spaces of Maps from a Riemann Surface to Complex Projective Space

Abstract

Let Map_d_∗(Mg, ℂP_n_−1) denote the space consisting of all basepoint preserving continuous maps of degree d from a compact Riemann surface Mg of genus g into a (n − 1)-dimensional complex projective space ℂP_n_−1. In this paper, we construct a finite dimensional configuration space model SP_n__d_(Mg) for the infinite dimensional space Map_d_∗(Mg, ℂP_n_−1) and show that the Atiyah–Jones type theorem (cf. [1], [12]) holds for this model.