"... when non-perturbative phenomena are included, there is no problem from the string theory point of view in effecting continuous transitions between Calabi-Yau spaces of different topology. This shows that stringy ideas about geometry are really more general than those found in classical Riemannian geometry. The moduli space of Calabi-Yau manifolds should thus be regarded as a continuously connected whole, rather than a series of different ones individually associated with different topological objects ... Thus, questions about the topology of Calabi-Yau spaces must be treated on the same footing as questions about the metric on the spaces. That is, the issue of topology is another aspect of the the moduli fields. These considerations are relevant to understanding the ground state of the universe."
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Gordon L. Kane, Malcolm J. Perry, and Anna N. Zytkow: ArXiv preprint
https://en.wikiquote.org/wiki/Calabi%E2%80%93Yau_manifold
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Calabi–Yau manifold
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