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# 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

#### 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