Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4

Abstract

We define Seiberg-Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4. When the foliation is taut, we show compactness of the moduli space under some hypothesis satisfied for instance by closed K-contact manifolds. Furthermore, we prove some vanishing and non-vanishing results and we highlight that the invariants may be used to distinguish different foliations on diffeomorphic manifolds.

To appear in Journal of Geometry and Physics. Final version

References in corpus (3)

• Energy-Momentum tensor on foliations
• Moduli Spaces of Contact Instantons
• On Park's exotic smooth four-manifolds

Cited by in corpus (8)

• A foliated Hitchin-Kobayashi correspondence
• The mean curvature of transverse Kähler foliations
• Basic Dolbeault cohomology and Weitzenböck frmulas on transversely Kähler foliations
• Index of transverse Dirac operator and cohomotopy Seiberg-Witten invariant for codimension $4$ Riemannian foliation
• Transverse ${\mathcal{F}}^T$-entropy and transverse Ricci flow for Riemannian foliations
• Direct sum for basic cohomology of codimension four taut Riemannian foliation
• A lift of the Seiberg-Witten equations to Kaluza-Klein 5-manifolds
• Monopole Floer homology for codimension-3 Riemannian foliation