Extra-twisted connected sum G_2-manifolds

TL;DR

This paper introduces a generalized construction of G_2-manifolds via quotients of building blocks, expanding the variety of topologies and enabling examples with disconnected moduli spaces of G_2 metrics.

Contribution

It extends Kovalev's twisted connected sum method by incorporating quotients, allowing for a broader class of G_2-manifolds with diverse topological types.

Findings

Constructed new G_2-manifolds with varied topologies

Demonstrated examples with disconnected moduli spaces

Generalized the twisted connected sum technique

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.