Truncated simplicial resolutions and spaces of rational maps. (English) Zbl 1237.58012

Mostovoy, Jacob

Q. J. Math. 63, No. 1, 181-187 (2012).

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