Coassociative submanifolds in Joyce's generalised Kummer constructions
Differential Geometry
2025-07-29 v2
Abstract
This article constructs coassociative submanifolds in -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 -manifold in which the metric degenerates. This forces the volume of the coassociatives to shrink to zero when the orbifold-limit is approached.
Cite
@article{arxiv.2305.05561,
title = {Coassociative submanifolds in Joyce's generalised Kummer constructions},
author = {Dominik Gutwein},
journal= {arXiv preprint arXiv:2305.05561},
year = {2025}
}
Comments
28 pages; This article is a revision of its published version, published in Pure and Applied Mathematics Quarterly Volume 20 (2024) Number 2. The current version corrects some typographical errors and mathematical inaccuracies and provides additional explanations and clarifications. Moreover, it rectifies two minor mistakes in Example 3.2 and Example 4.9