Global analysis, analysis on manifolds Singularities of smooth maps Concept
Infinitesimal stability
Summary
A smooth map is infinitesimally stable if every infinitesimal deformation of it can be undone. The undoing uses infinitesimal changes of coordinates in the source and in the target. It is the linearised form of stability: an equation for vector fields replaces a condition on diffeomorphisms. Mather's theorem says that for proper maps the two notions agree. This turns stability into a problem of linear algebra over rings of smooth functions.
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| Tag | C3TFCVE2YK |
|---|---|
| URI | m2://C3TFCVE2YK |
| Kind | concept |
| Writing | W0 stub |
| MSC | 58K25, 57R45 |
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