An Invariant for Transverse Coassociative 4-Folds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908600901828608 |
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| author | Galt, Dylan |
| author_facet | Galt, Dylan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Invariant for Transverse Coassociative 4-Folds Galt, Dylan Differential Geometry 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. |
| title | An Invariant for Transverse Coassociative 4-Folds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.10193 |