Spin(7)-Orbifold Resolutions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916963224125440 |
|---|---|
| author | Majewski, Viktor F. |
| author_facet | Majewski, Viktor F. |
| contents | We establish a general analytic and geometric framework for resolving Spin(7)--orbifolds. These spaces arise naturally as boundary points in the moduli space of exceptional holonomy metrics, and smooth Gromov--Hausdorff resolutions can be viewed as paths from the boundary to the interior of the moduli space. Our construction combines algebraic and symplectic techniques with analytic gluing methods: singular strata are replaced by families of adiabatic torsion--free, asymptotically conical fibred spaces whose existence is controlled by the analysis of Dirac--type operators on orbifold resolutions. We formulate obstruction conditions in terms of string cohomology, prove existence results for torsion--free Spin(7)--structures extending Joyce's theorem arXiv:math/9910002 to the setting of orbifold resolutions, and construct new families of compact Spin(7)--manifolds. By dimensional reduction, our results also recover, generalise and extend the results of Joyce and Karigiannis arXiv:1707.09325 on $G_2$--orbifold resolutions. This unifies and extends all known resolution methods for exceptional holonomy orbifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spin(7)-Orbifold Resolutions Majewski, Viktor F. Differential Geometry 58J05, 58A35, 53C26, 53C25 We establish a general analytic and geometric framework for resolving Spin(7)--orbifolds. These spaces arise naturally as boundary points in the moduli space of exceptional holonomy metrics, and smooth Gromov--Hausdorff resolutions can be viewed as paths from the boundary to the interior of the moduli space. Our construction combines algebraic and symplectic techniques with analytic gluing methods: singular strata are replaced by families of adiabatic torsion--free, asymptotically conical fibred spaces whose existence is controlled by the analysis of Dirac--type operators on orbifold resolutions. We formulate obstruction conditions in terms of string cohomology, prove existence results for torsion--free Spin(7)--structures extending Joyce's theorem arXiv:math/9910002 to the setting of orbifold resolutions, and construct new families of compact Spin(7)--manifolds. By dimensional reduction, our results also recover, generalise and extend the results of Joyce and Karigiannis arXiv:1707.09325 on $G_2$--orbifold resolutions. This unifies and extends all known resolution methods for exceptional holonomy orbifolds. |
| title | Spin(7)-Orbifold Resolutions |
| topic | Differential Geometry 58J05, 58A35, 53C26, 53C25 |
| url | https://arxiv.org/abs/2509.16057 |