Associative submanifolds in twisted connected sum $G_2$-manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910108027453440 |
|---|---|
| author | Bera, Gorapada |
| author_facet | Bera, Gorapada |
| contents | We introduce a method to construct closed rigid associative submanifolds in twisted connected sum $G_2$-manifolds. More precisely, we prove a gluing theorem of asymptotically cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds under a transverse intersection hypothesis. This is analogous to the gluing theorem for $G_2$-instantons introduced in [SW15]. We rephrase the hypothesis in the special cases where the ACyl associative submanifolds are obtained from holomorphic curves or special Lagrangians in ACyl Calabi-Yau $3$-folds, in terms of algebraic-geometric conditions and topological conditions, respectively. This yields many rigid associative submanifolds with new topological types $S^3$, $\mathbf R\mathbf P^3$ or $\mathbf R\mathbf P^3\#\mathbf R\mathbf P^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Associative submanifolds in twisted connected sum $G_2$-manifolds Bera, Gorapada Differential Geometry We introduce a method to construct closed rigid associative submanifolds in twisted connected sum $G_2$-manifolds. More precisely, we prove a gluing theorem of asymptotically cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds under a transverse intersection hypothesis. This is analogous to the gluing theorem for $G_2$-instantons introduced in [SW15]. We rephrase the hypothesis in the special cases where the ACyl associative submanifolds are obtained from holomorphic curves or special Lagrangians in ACyl Calabi-Yau $3$-folds, in terms of algebraic-geometric conditions and topological conditions, respectively. This yields many rigid associative submanifolds with new topological types $S^3$, $\mathbf R\mathbf P^3$ or $\mathbf R\mathbf P^3\#\mathbf R\mathbf P^3$. |
| title | Associative submanifolds in twisted connected sum $G_2$-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2209.00156 |