Relation To The Brouwer Fixed Point Theorem
The Lefschetz fixed point theorem generalizes the Brouwer fixed point theorem, which states that every continuous map from the n-dimensional closed unit disk Dn to Dn must have at least one fixed point.
This can be seen as follows: Dn is compact and triangulable, all its homology groups except H0 are 0, and every continuous map f : Dn → Dn induces a non-zero homomorphism f* : H0(Dn, Q) → H0(Dn, Q); all this together implies that Λf is non-zero for any continuous map f : Dn → Dn.
Read more about this topic: Lefschetz Fixed-point Theorem
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