Abstract
Any Calabi-Yau threefold X with infinite fundamental group admits an étale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. We call X of type A in the former case and of type K in the latter case. In this paper, we provide the full classification of Calabi-Yau threefolds of type K, based on Oguiso and Sakurai's work. Together with a refinement of Oguiso and Sakurai's result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau threefolds with infinite fundamental group.
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