Quantum creation of a universe with an S1℗Tg spatial topology is considered. Using both the Euclidean functional integral and the tunneling approach as prescriptions applied to quantum cosmology, we calculate the wave function of such a universe with a negative cosmological constant and without matter. The anisotropic minisuperspace path integral is calculated in the semiclassical approximation, and it is shown that the wave function is proportional to the genus of the two-dimensional compact the probability of quantum creation of a higher-genus universe, and it appears that in Hartle-Hawking approach the probability of creation increases with the genus g, while in the tunneling approach it decreases with g.