Last Updated
：2025/12/04
Atiyah-Singer index theorem
Proper noun
Japanese Meaning
コンパクト多様体上の楕円型微分作用素に対して、解空間の次元に関連する解析的指数と、位相的な性質に基づいて定義される位相的指数が一致することを示す定理。
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(differential geometry) A theorem stating that, for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
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Atiyah-Singer index theorem
In my seminar, I explained how the Atiyah-Singer index theorem links the analytical properties of elliptic differential operators to topological invariants of compact manifolds.
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In my seminar, I explained how the Atiyah-Singer index theorem links the analytical properties of elliptic differential operators to topological invariants of compact manifolds.
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