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If the Universe undergoes a phase transition, at which global monopoles are created or destroyed, topology of its spatial sections can change.
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From Bergmann’s work Bergmann:1981 it follows that a time-dependent change in κ \kappa can be realized by a space-like heat flow. It is, however, unclear whether such a flow can be realized in a realistic setting
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J. J. Levin, “Topology and the cosmic microwave background,” Phys. Rept. 365
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J. P. Uzan, R. Lehoucq and J. P. Luminet, “New developments in the search for the topology of the universe,” [gr-qc/0005128]
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