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https://hdl.handle.net/2440/136854
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DC Field | Value | Language |
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dc.contributor.author | Baraglia, D. | - |
dc.contributor.author | Hekmati, P. | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Advances in Mathematics, 2022; 408:108661-1-108661-47 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.issn | 1090-2082 | - |
dc.identifier.uri | https://hdl.handle.net/2440/136854 | - |
dc.description.abstract | 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 Sasakian 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. | - |
dc.description.statementofresponsibility | David Baraglia, Pedram Hekmati | - |
dc.language.iso | en | - |
dc.publisher | Elsevier | - |
dc.rights | © 2022 Elsevier Inc. All rights reserved. | - |
dc.source.uri | http://dx.doi.org/10.1016/j.aim.2022.108661 | - |
dc.subject | Hitchin-Kobayashi; Foliations; Stable bundles; Hermitian-Einstein | - |
dc.title | A foliated Hitchin-Kobayashi correspondence | - |
dc.type | Journal article | - |
dc.identifier.doi | 10.1016/j.aim.2022.108661 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP110103745 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP170101054 | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Baraglia, D. [0000-0002-8450-1165] | - |
Appears in Collections: | Mathematical Sciences publications |
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