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Dimensional reduction on multiply connected homogeneous spaces.

We study the dimensional reduction of a gauge theory determined in a (4+{ital d})-dimensional space to the space {ital M}{sup 4}{direct product}{ital S}/{ital R} in the case when {ital S}/{ital R} is a multiply connected homogeneous compact {ital d}-dimensional space. A classification of all possible multiply connected homogeneous spaces {ital S}/{ital 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.