Twisted connected sums and special Riemannian holonomy
Abstract
We give a new, connected-sum-like construction of Riemannian metrics with special holonomy G2 on compact 7-manifolds. The construction is based on a gluing theorem for appropriate elliptic partial differential equations. As a prerequisite, we also obtain asymptotically cylindrical Riemannian manifolds with holonomy SU(3) building up on the work of Tian and Yau. Examples of new topological types of compact 7-manifolds with holonomy G2 are constructed using Fano 3-folds.
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