Global analysis, analysis on manifolds Differential operators on manifolds Concept
Elliptic complex
Summary
An elliptic complex is a sequence of differential operators between vector bundles whose consecutive composites vanish. Its principal symbols must form an exact sequence at each nonzero covector. It generalises an elliptic operator, which is an elliptic complex of length two. On a compact manifold its cohomology groups are finite-dimensional, and its index is their alternating sum of dimensions. The de Rham complex and the Dolbeault complex are the basic examples.
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| Tag | M8GMH8GQR6 |
|---|---|
| URI | m2://M8GMH8GQR6 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 58J10, 58J20 |
| Same as |
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