Simplicial resolutions and spaces of algebraic maps between real projective spaces

2011/09/02 by Kozlowski, Andrzej, Yamaguchi, Kohhei
#55P10 #55P35 #55R80 #55T99 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.0352

Abstract

We show that the space 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 \RPⁿ) of continuous maps from the m-dimensional real projective space \RP^m into the n real dimensional projective space \RPⁿ up to dimension %in dimensions smaller than (n-m)(d+1)-1. This considerably improves the main result of \citeAKY1.

Related

• Spaces of algebraic and continuous maps between real algebraic varieties
• Spaces of polynomials with constrained real divisors, II. (Co)homology & stabilization
• Spaces of algebraic maps from real projective spaces into complex projective spaces
• Homology of spaces of homogeneous polynomials in R² without multiple zeros
• Spaces of equivariant algebraic maps from real projective spaces into complex projective spaces