Extra-twisted connected sum G_2-manifolds
arXiv:1809.09083
Abstract
We present a construction of closed 7-manifolds of holonomy G_2, which generalises Kovalev's twisted connected sums by taking quotients of the pieces in the construction before gluing. This makes it possible to realise a wider range of topological types, and Crowley, Goette and the author arXiv:1505.02734 use this to exhibit examples of closed 7-manifolds with disconnected moduli space of holonomy G_2 metrics.
65 pages, 16 figures. v3: Small corrections. To appear in Ann. Glob. Anal. Geom