Pure and Applied Mathematics Quarterly

Volume 20 (2024)

Number 2

Coassociative submanifolds in Joyce's generalised Kummer constructions

Pages: 923 – 954

DOI: https://dx.doi.org/10.4310/PAMQ.2024.v20.n2.a7

Author

Dominik Gutwein (Humboldt-Universität zu Berlin, Germany)

Abstract

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.

The full text of this article is unavailable through your IP address: 3.15.138.214

Received 2 July 2023

Accepted 9 October 2023

Published 3 April 2024