Homology, Homotopy and Applications
Volume 16 (2014)
Complexification and homotopy
Pages: 159 – 165
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 $\beta(Y)$.
real algebraic variety, regular map, homotopy, complexification
2010 Mathematics Subject Classification