2012

G_2-manifolds and associative submanifolds via semi-Fano 3-folds

Corti, Alessio, Haskins, Mark, Nordström, Johannes et al.

Understand

We provide a significant extension of the twisted connected sum construction of G_2-manifolds, i.e.

Riemannian 7-manifolds with holonomy group G_2, first developed by Kovalev; along the way we address some foundational questions at the heart of the twisted connected sum construction.
Some of the main contributions of the paper are: (i) We correct, clarify and extend several aspects of the K3 "matching problem" that occurs as a key step in the twisted connected sum construction.
(ii) We show that the large class of asymptotically cylindrical Calabi-Yau 3-folds built from semi-Fano 3-folds (a subclass of weak Fano 3-folds) can be used as components in the twisted connected sum construction.

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