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arXiv · 2410.10193

An Invariant for Transverse Coassociative 4-Folds

Dylan Galt
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Abstract

We define a $\mathbb{Z}_2$-valued invariant for transversely-intersecting coassociative $4$-folds equipped with spin structures. Our main result shows this invariant provides an obstruction to separating two such coassociatives through a family of transverse coassociative deformations. We further prove that there is a canonical generalized connected sum of two such transverse coassociatives whose diffeomorphism type is determined by our invariant. When one coassociative is a graph over the other, we relate our invariant to the parity function in near-symplectic geometry. Finally, we discuss conjectural consequences for non-compactness phenomena and compute our invariant for the $Sp(1)$-invariant coassociatives discovered by Harvey and Lawson.

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Dylan Galt. 2024-10-14. An Invariant for Transverse Coassociative 4-Folds. https://arxiv.org/abs/2410.10193

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