Where does foliation collide?

In structural geology, foliation is any repeated planar fabric that metamorphism imprints on a rock, such as the parallel alignment of platy minerals or the segregation of light and dark layers, produced as the rock recrystallises and flows under directed stress. Fletcher's 1977 Quantitative theory for metamorphic differentiation in the development of crenulation cleavage modelled how such layering self-organises when an existing fabric is shortened. The referent is a pervasive planar anisotropy in a deformed rock, and it is unrelated to the mathematician's decomposition of a space that happens to share the name, beyond the common image of a thing split into leaves.[1]

Unit

The orientation and spacing of the planar fabric within a deformed rock

Recovery means

Not applicable

Measured by

Recorded by the strike and dip of the fabric, its intensity, and the preferred orientation of platy minerals in thin section

In differential topology, a foliation is a way of decomposing a manifold into a family of connected, parallel submanifolds called leaves, all of the same dimension, that fit together locally like the pages of a book or the flat layers of a stack. Lawson's 1974 survey Foliations in the Bulletin of the American Mathematical Society laid out when a manifold admits such a structure and how the leaves behave globally. The word was borrowed from the geologist's layered rock, but the construct is an abstract partition of a space governed by an integrable distribution of tangent planes, with nothing of stress, mineral, or recrystallisation about it.[2]

Unit

The dimension of the leaves and the codimension of the foliation on a manifold

Recovery means

Not applicable

Measured by

Characterised by the codimension, the holonomy of the leaves, and whether an integrable tangent distribution exists