In string theory, we compactify a 10-dimensional space by a Calabi-Yau 3-fold to reduce the dimension to 4. To get a reasonable theory, a Calabi-Yau 3-fold should satisfy some properties. One is the Euler number must be $\pm6$ so that it is compatible with the generation of the elementary particles.
I heard that the fundamental group of the Calabi-Yau 3-fold should not be trivial. What should it be?