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<p>Motivated by problems in the study of Anosov and pseudo-Anosov flows on 3-manifolds, we characterize when a pair <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3200_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^+, L^-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>L</mi> <mo>-</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> of subsets of laminations of the circle can be <i>completed</i> to a pair of transverse foliations of the plane or, separately, realized as the endpoints of such a <i>bifoliation</i> of the plane. (We allow also singular bifoliations with simple prongs, as those arising in pseudo-Anosov flows). This program is carried out at a level of generality applicable to bifoliations coming from pseudo-Anosov flows with and without perfect fits, as well as many other examples, and is natural with respect to group actions preserving these structures.</p>

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Completing prelaminations

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Thomas Barthelmé,
  • Christian Bonatti,
  • Kathryn Mann

摘要

Motivated by problems in the study of Anosov and pseudo-Anosov flows on 3-manifolds, we characterize when a pair \(L^+, L^-\) L + , L - of subsets of laminations of the circle can be completed to a pair of transverse foliations of the plane or, separately, realized as the endpoints of such a bifoliation of the plane. (We allow also singular bifoliations with simple prongs, as those arising in pseudo-Anosov flows). This program is carried out at a level of generality applicable to bifoliations coming from pseudo-Anosov flows with and without perfect fits, as well as many other examples, and is natural with respect to group actions preserving these structures.