The $\barν$-Invariant of $G_2$-Structures on Aloff-Wallach Spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908939929518080 |
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| author | Aleshin, Artem |
| author_facet | Aleshin, Artem |
| contents | We compute the $\barν$-invariant of homogeneous nearly-parallel $G_2$-structures on Aloff--Wallach spaces $N_{k,l} = SU(3)/S^1_{k,l}$. Using Goette's formulas for the $η$-invariants of homogeneous spaces, we derive an explicit expression for $\barν$ in terms of representation-theoretic data and show that for the two homogeneous nearly-parallel structures $φ^\pm$ on $N_{k,l}$ one has \[\barν(φ^\pm) = \mp 41.\] Additionally, we compare the $\barν$-invariants of the nearly-parallel $G_2$-structures arising from the 3-Sasakian structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $\barν$-Invariant of $G_2$-Structures on Aloff-Wallach Spaces Aleshin, Artem Differential Geometry We compute the $\barν$-invariant of homogeneous nearly-parallel $G_2$-structures on Aloff--Wallach spaces $N_{k,l} = SU(3)/S^1_{k,l}$. Using Goette's formulas for the $η$-invariants of homogeneous spaces, we derive an explicit expression for $\barν$ in terms of representation-theoretic data and show that for the two homogeneous nearly-parallel structures $φ^\pm$ on $N_{k,l}$ one has \[\barν(φ^\pm) = \mp 41.\] Additionally, we compare the $\barν$-invariants of the nearly-parallel $G_2$-structures arising from the 3-Sasakian structure. |
| title | The $\barν$-Invariant of $G_2$-Structures on Aloff-Wallach Spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.04605 |