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Truncated simplicial resolutions and spaces of rational maps. (English) Zbl 1237.58012
Summary: We show that whenever \(m \leq n\), the space of all continuous rational maps from \(\mathbb{C}\mathbb{P}^{m}\) to \(\mathbb{C}\mathbb{P}^{n}\) has the same homology as the space of all continuous maps between these spaces in dimensions smaller than \(d(2n - 2m + 1) - 1\). This improves the result of the author’s paper [Topology 45, No. 2, 281–293 (2006; Zbl 1086.58005)].

MSC:
58D15 Manifolds of mappings
55P10 Homotopy equivalences in algebraic topology
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