## Homology, Homotopy and Applications

### Complexification and homotopy

#### 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 $\beta(Y)$.

#### Article information

Source
Homology Homotopy Appl., Volume 16, Number 1 (2014), 159-165.

Dates
First available in Project Euclid: 3 June 2014