Mathematics – Geometric Topology
Scientific paper
2011-08-03
Mathematics
Geometric Topology
This version has minor changes in the introduction and bibliography
Scientific paper
This paper extends and simplifies our paper "Foliation Cones" (KirbyFest, 1999) while correcting some errors. We classify finite depth, foliated 3-manifolds M with a given "substructure" S. The components W of (M \ S) are stably foliated and the possible such foliations are classified, up to isotopy, by the rays through the integer lattice points in the interiors of finitely many closed, convex, non-overlapping, finite-sided, polyhedral cones in a suitable cohomology of W. While the cones are generally infinite dimensional, they have only finitely many faces. Results of this type are given both for the cases that the foliation is, and is not, smooth.
Cantwell John
Conlon Lawrence
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