Singularity theory

For non-mathematical singularity theories, see singularity.

How singularities may arise

In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds (spaces without singularities) may acquire special, singular points by a number of routes. Projection is one way, very obvious in visual terms when three-dimensional objects are projected into two dimensions (for example in one of our eyes); in looking at classical statuary the folds of drapery are amongst the most obvious features. Singularities of this kind include caustics, very familiar as the light patterns at the bottom of a swimming pool.

Related Topics:
Projection - Eye - Folds - Caustic - Swimming pool

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Other ways in which singularities occur is by degeneration of manifold structure. That implies the breakdown of parametrization of points; it is prominent in cosmology, where a gravitational singularity, at which the gravitational field is strong enough to change the very structure of space-time, is identified with a black hole. In a less dramatic fashion, the presence of symmetry can be good cause to consider orbifolds, which are manifolds that have acquired 'corners' in a process of folding up resembling the creasing of a table napkin.

Related Topics:
Degeneration - Parametrization - Cosmology - Gravitational singularity - Gravitational field - Space-time - Black hole - Symmetry - Orbifold - Table napkin

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