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We study the dimensional reduction of a gauge theory determined in a (4fd)-dimensional space to the space M ' @ S / R in the case when S / R is a multiply connected homogeneous compact ddimensional space. A classification of all possible multiply connected homogeneous spaces S / R is given and their maximum nonconnectedness groups are determined. The corresponding breaking of the gauge symmetry which is a generalization of the standard scheme of dimensional reduction on coset spaces and of the Hosotani mechanism is investigated.

Quantum creation of universes is considered within the framework of linear D-dimensional third quantized gravity with non-abelian gauge fields. It is shown that the number density of universes is infinitely peaked up on a sequence of compactified universes Sn+1×Id, where dimensionality of compact internal space Id takes values d=0, 1, …, D−3 and effective n+1-dimensional cosmological constant tends to zero, Sn+1→Mn+1.

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