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arXiv · 2202.00522

Associative submanifolds in Joyce's generalised Kummer constructions

Shubham Dwivedi·Daniel Platt·Thomas Walpuski
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Abstract

This article constructs examples of associative submanifolds in $G_2$-manifolds obtained by resolving $G_2$-orbifolds using Joyce's generalised Kummer construction. As the $G_2$-manifolds approach the $G_2$-orbifolds, the volume of the associative submanifolds tends to zero. This partially verifies a prediction due to Halverson and Morrison.

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Shubham Dwivedi, Daniel Platt, Thomas Walpuski. 2022-02-01. Associative submanifolds in Joyce's generalised Kummer constructions. https://doi.org/10.1007/s00220-023-04716-7

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