On singular foliations on the solid torus

Arraut, José; Martins, Luciana; Schuetz, Dirk

Abstract

We study smooth foliations on the solid torus S1×D2S1×D2 having S1×{0}S1×{0} and S1×∂D2S1×∂D2 as the only compact leaves and S1×{0}S1×{0} as singular set. We show that all other leaves can only be cylinders or planes, and give necessary conditions for the foliation to be a suspension of a diffeomorphism of the disc.

Citation

Arraut, J., Martins, L., & Schuetz, D. (2013). On singular foliations on the solid torus. Topology and its Applications, 160(13), 1659-1674. https://doi.org/10.1016/j.topol.2013.06.012

• Journal Article Type: Article
• Acceptance Date: Jun 28, 2013
• Publication Date: Aug 15, 2013
• Deposit Date: Jun 29, 2015
• Publicly Available Date: Jul 7, 2015
• Journal: Topology and its Applications
• Print ISSN: 0166-8641
• Electronic ISSN: 1879-3207
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 160
• Issue: 13
• Pages: 1659-1674
• DOI: https://doi.org/10.1016/j.topol.2013.06.012
• Keywords: Foliations, Solid torus, Vector fields.
• Public URL: https://durham-repository.worktribe.com/output/1435340