A foliated Hitchin-Kobayashi correspondence
| Autor: | Baraglia, David, Hekmati, Pedram |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Adv. Math. 408 (2022), 108661 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2022.108661 |
| Popis: | We prove an analogue of the Hitchin-Kobayashi correspondence for compact, oriented, taut Riemannian foliated manifolds with transverse Hermitian structure. In particular, our Hitchin-Kobayashi theorem holds on any compact Sasakian manifold. We define the notion of stability for foliated Hermitian vector bundles with transverse holomorphic structure and prove that such bundles admit a basic Hermitian-Einstein connection if and only if they are polystable. Our proof is obtained by adapting the proof by Uhlenbeck and Yau to the foliated setting. We relate the transverse Hermitian-Einstein equations to higher dimensional instanton equations and in particular we look at the relation to higher contact instantons on Sasaki manifolds. For foliations of complex codimension 1, we obtain a transverse Narasimhan-Seshadri theorem. We also demonstrate that the weak Uhlenbeck compactness theorem fails in general for basic connections on a foliated bundle. This shows that not every result in gauge theory carries over to the foliated setting. Comment: 42 pages |
| Databáze: | arXiv |
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