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Let Mapd(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 CPn−1. In this paper, we construct a finite dimensional configuration space model SPn(M ′ g) for the infinite dimensional space Mapd(Mg,CP n−1) and show that the Atiyah-Jones type theorem (cf. [1], [12]) holds for this model. §

Configuration space models for spaces of maps from a Riemann surface to complex projective space