Singularity theory

For non-mathematical singularity theories, see singularity.

Other possible meanings

The theory mentioned above does not directly relate to the concept of mathematical singularity as a value at which a function isn't defined. For that, see for example isolated singularity, essential singularity, removable singularity. The monodromy theory of differential equations, in the complex domain, around singularities, does however come into relation with the geometric theory. Roughly speaking, monodromy studies the way a covering map can degenerate, while singularity theory studies the way a manifold can degenerate; and these fields are linked.

Related Topics:
Mathematical singularity - Isolated singularity - Essential singularity - Removable singularity - Monodromy - Differential equation - Covering map

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See also:

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• Tangent
• Zariski tangent space
• General position
• Contact (mathematics)
• Singular solution
• Folding, origami tech tree
• Stratification
• Intersection homology
• Mixed Hodge structure