A foliation decomposes a topological manifold into connected leaves which locally look like parallel slices in product coordinate charts.
A codimension-one foliation of a closed three-manifold is taut if every leaf meets a closed transverse curve. In particular, the fibers of a bundle over form a taut foliation.
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Foliation is a term that can refer to different concepts depending on the context, primarily in geology and botany. Here are the key meanings: 1. **Geology**: In geology, foliation refers to the parallel layering that can occur in metamorphic rocks due to the alignment of mineral grains under directional pressure. This structure is typically produced by processes such as metamorphism, where heat and pressure cause the minerals in the rock to recrystallize and realign.