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.