تقرير
Strong generalized holomorphic principal bundles
| العنوان: | Strong generalized holomorphic principal bundles |
|---|---|
| المؤلفون: | Pal, Debjit, Poddar, Mainak |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Complex Variables, Mathematics - Symplectic Geometry, Primary: 53D18, 32L05, 32L20. Secondary: 57R22, 57R30, 53D05 |
| الوصف: | We introduce the notion of a strong generalized holomorphic (SGH) fiber bundle and develop connection and curvature theory for an SGH principal $G$-bundle over a regular generalized complex (GC) manifold, where $G$ is a complex Lie group. We develop a de Rham cohomology for regular GC manifolds, and a Dolbeault cohomology for SGH vector bundles. Moreover, we establish a Chern-Weil theory for SGH principal $G$-bundles under certain mild assumptions on the leaf space of the GC structure. We also present a Hodge theory along with associated dualities and vanishing theorems for SGH vector bundles. Several examples of SGH fiber bundles are given. Comment: 73 pages, minor revision, comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.18113 |
| رقم الأكسشن: | edsarx.2404.18113 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |