##  [Lefschetz Fixed-Point Theorem](/lefschetz-fixed-point-theorem) 

  ##  [Lefschetz Fixed-Point Theorem](https://puremath.quantumdictionary.io/lefschetz-fixed-point-theorem-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem relating algebraic invariants to fixed points: for a continuous map f of a compact, triangulable (or more generally a compact ANR) space, the Lefschetz number L(f), computed as an alternating sum of traces of the induced maps f_* on homology, detects fixed points — if L(f)≠0 then f has at least one fixed point.