# Commentarii Mathematici Helvetici

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**Volume 84, Issue 1, 2009, pp. 127–134**

**DOI: 10.4171/CMH/154**

Published online: 2009-03-31

Transcendental submanifolds of projective space

Wojciech Kucharz^{[1]}(1) Jagiellonian University, Krakow, Poland

Given integers `m` and `c` satisfying `m` − 2 ≥ `c` ≥ 2, we
explicitly construct a nonsingular `m`-dimensional algebraic subset
of ℙ^{m + c}(ℝ) that is not isotopic to the set
of real points of any nonsingular complex algebraic subset of
ℙ^{m + c}(ℂ) defined over ℝ. The
first examples of this type were obtained by Akbulut and King in a
more complicated and nonconstructive way, and only for certain large
integers `m` and `c`.

*Keywords: *Smooth manifold, algebraic set, isotopy

Kucharz Wojciech: Transcendental submanifolds of projective space. *Comment. Math. Helv.* 84 (2009), 127-134. doi: 10.4171/CMH/154