Simplicial resolutions and spaces of algebraic maps between real projective spaces

Details Simplicial resolutions and spaces of algebraic maps between real projective spaces Simplicial resolutions and spaces of algebraic maps between real projective spaces

2011-09-02

arxiv.org/abs/1109.0352v1

Mathematics

Algebraic Topology

Scientific paper

We show that the space $\tilde{A}_{d}(m,n)$ consisting of all real projective classes of $(n+1)$-tuples of real coefficients homogeneous polynomials of degree $d$ in $(m+1)$ variables, without common real roots except zero, has the same homology as the space $ \Map(\RP^m,\Bbb \RP^n)$ of continuous maps from the $m$-dimensional real projective space $\RP^m$ into the $n$ real dimensional projective space $\RP^n$ up to dimension %in dimensions smaller than $(n-m)(d+1)-1$. This considerably improves the main result of \cite{AKY1}.

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