Coassociative submanifolds in Joyce's generalised Kummer constructions

This article constructs coassociative submanifolds in $\mathrm{G}_2$-manifolds arising from Joyce’s generalised Kummer construction. The novelty compared to previous constructions is that these submanifolds all lie within the critical region of the $\mathrm{G}_2$-manifold in which the metric degenerates. This forces the volume of the coassociatives to shrink to zero when the orbifold-limit is approached.

Keywords

coassociative submanifolds, $\mathrm{G}_2$-manifolds, generalised Kummer constructions

2010 Mathematics Subject Classification

Primary 53C38. Secondary 53C25, 53C29.

Full Text (PDF format)

Received 2 July 2023

Accepted 9 October 2023

Published 3 April 2024