Homology, Homotopy and Applications

Complexification and homotopy

Wojciech Kucharz and Łukasz Maciejewski

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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

Permanent link to this document
https://projecteuclid.org/euclid.hha/1401800077

Mathematical Reviews number (MathSciNet)
MR3197976

Zentralblatt MATH identifier
1327.14239

Subjects
Primary: 14P05: Real algebraic sets [See also 12D15, 13J30] 14P25: Topology of real algebraic varieties

Keywords
Real algebraic variety regular map homotopy complexification

Citation

Kucharz, Wojciech; Maciejewski, Łukasz. Complexification and homotopy. Homology Homotopy Appl. 16 (2014), no. 1, 159--165. https://projecteuclid.org/euclid.hha/1401800077


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