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dc.contributor.authorClark, Alex
dc.contributor.authorHurder, Steven
dc.date.accessioned2012-03-02T20:10:12Z
dc.date.available2012-03-02T20:10:12Z
dc.date.issued2011-04-27
dc.identifier.bibliographicCitationClark, A. & Hurder, S. 2011. Embedding solenoids in foliations. Topology and Its Applications, 158(11): 1249-1270. DOI: 10.1016/j.topol.2011.04.010en
dc.identifier.issn0166-8641
dc.identifier.otherDOI: 10.1016/j.topol.2011.04.010
dc.identifier.urihttp://hdl.handle.net/10027/8156
dc.descriptionNOTICE: this is the author’s version of a work that was accepted for publication in Topology and Its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Topology and Its Applications,158 (11), 2011 DOI: 10.1016/j.topol.2011.04.010 The original publication is available at www.elsevier.com.en
dc.description.abstractIn this paper we find smooth embeddings of solenoids in smooth foliations. We show that if a smooth foliation F of a manifold M contains a compact leaf L with H1(L; R) not equal to 0 and if the foliation is a product foliation in some saturated open neighborhood U of L, then there exists a foliation F on M which is C1-close to F, and F has an uncountable set of solenoidal minimal sets contained in U that are pairwise non-homeomorphic. If H1(L; R) is 0, then it is known that any sufficiently small perturbation of F contains a saturated product neighborhood. Thus, our result can be thought of as an instability result complementing the stability results of Reeb, Thurston and Langevin and Rosenberg. © 2011 Elsevier B.V. All rights reserved.en
dc.description.sponsorshipAlex Carter was supported in part by EPSRC grant EP/G006377/1. Steven Hurder was supported in part by NSF Grant 0406254.en
dc.language.isoen_USen
dc.publisherElsevieren
dc.subjectsolenoiden
dc.subjectfoliationen
dc.titleEmbedding solenoids in foliationsen
dc.typeArticleen


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