Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Complexification and homotopy

Pages: 159 – 165

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n1.a9

Authors

Wojciech Kucharz (Department of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza, Kraków, Poland)

Łukasz Maciejewski (Department of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza, Kraków, Poland)

Abstract

Let $Y$ be a real algebraic variety. We are interested in determining the supremum, $\beta(Y)$, of all nonnegative integers $n$ with the following property: For every $n$-dimensional compact connected nonsingular real algebraic variety $X$, every continuous map from $X$ into $Y$ is homotopic to a regular map. We give an upper bound for $\beta(Y)$, based on a construction involving complexification of real algebraic varieties. In some cases, we obtain the exact value of $\beta(Y)$.

Keywords

real algebraic variety, regular map, homotopy, complexification

2010 Mathematics Subject Classification

14P05, 14P25

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