Lefschetz fixed-point theorem

Proper noun

(mathematics) A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X.

Japanese Meaning

コンパクトな位相空間 X 上の連続写像に対して、その写像により誘導されるホモロジー群上の写像のトレースを用い、不変点（固定点）の数を計算するための公式。

What is this buttons?

In algebraic topology seminars, the Lefschetz fixed-point theorem is often presented as a powerful tool that counts fixed points of a continuous self-map of a compact space via traces on the induced homology maps.

Google Translation / DeepL Translation

代数的トポロジーのセミナーでは、レフシェッツの不動点定理は、コンパクトな位相空間への連続な自己写像の不動点を、ホモロジー群に誘導される写像の跡（トレース）を用いて数える強力な手法としてしばしば紹介される。

Details

Sense（1）

(mathematics) A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X.

the Lefschetz fixed-point theorem

（ canonical ）

Details

Lefschetz fixed-point theorem

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