JournalsprimsVol. 39, No. 3pp. 535–543

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

  • Kohhei Yamaguchi

    University of Electro-Communications, Tokyo, Japan
Configuration Space Models for Spaces of Maps from a Riemann Surface to Complex Projective Space cover
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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.

Cite this article

Kohhei Yamaguchi, Configuration Space Models for Spaces of Maps from a Riemann Surface to Complex Projective Space. Publ. Res. Inst. Math. Sci. 39 (2003), no. 3, pp. 535–543

DOI 10.2977/PRIMS/1145476078