Extra-twisted connected sum \(G_2\)-manifolds

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 use this to exhibit examples of closed 7-manifolds with disconnected moduli space of holonomy \(G_2\) metrics.