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      Spaces of equivariant algebraic maps from real projective spaces into complex projective spaces

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          Abstract

          We study the homotopy types of certain spaces closely related to the spaces of algebraic (rational) maps from the \(m\) dimensional real projective space into the \(n\) dimensional complex projective space for \(2\leq m\leq 2n\) (we conjecture this relation to be a homotopy equivalence). In an earlier article we proved that the homotopy types of the terms of the natural degree filtration approximate closer and closer the homotopy type of the space of continuous maps and obtained bounds that describe the closeness of the approximation in terms of the degrees of the maps. Here we improve the estimates of the bounds by using new methods introduced in \cite{Mo3} and used in \cite{KY4}. In addition, in the the last section, we prove a special case (\(m=1\)) of the conjecture stated in \cite{AKY1} that our spaces are homotopy equivalent to the spaces of algebraic maps.

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          The topology of spaces of rational functions

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            Topology of complements of discriminants and resultants

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              Spaces of rational maps and the Stone–Weierstrass theorem

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                Author and article information

                Journal
                02 September 2011
                Article
                1109.0353
                aa5e486c-13ce-4888-a0b0-b63b29d9a729

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                26C15, 55P35, 55P91
                math.AT

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