Open Saturated Sets Without Holonomy

John Cantwell; Lawrence Conlon

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arXiv · 1108.0714

Open Saturated Sets Without Holonomy

John Cantwell·Lawrence Conlon

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Abstract

Open, connected, saturated sets W without holonomy in codimension one foliations play key roles as fundamental building blocks. Here, for the case of foliated 3-manifolds, we produce a finite system of closed, convex, non-overlapping polyhedral cones in the first cohomology of W with real coefficients such that the isotopy classes of possible foliations of W without holonomy, either dense leaved in W or proper, correspond one-to-one to the rays in the interiors of these cones. This generalizes our classification of depth one foliations to foliations of finite depth and more general foliations.

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BibTeX RIS

John Cantwell, Lawrence Conlon. 2011-08-03. Open Saturated Sets Without Holonomy. https://arxiv.org/abs/1108.0714

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