Editing Lefschetz fixed-point theorem (section)

==Relation to the Euler characteristic==
The Lefschetz number<ref name="EncLNumbers">{{cite web|access-date=2025-01-11 |title=Lefschetz number - Encyclopedia of Mathematics |url=https://encyclopediaofmath.org/wiki/Lefschetz_number |website=encyclopediaofmath.org}}<!-- auto-translated from Polish by Module:CS1 translator --></ref> of the [[identity function|identity map]] on a finite [[CW complex]] can be easily computed by realizing that each <math>f_\ast</math> can be thought of as an [[identity matrix]], and so each trace term is simply the dimension of the appropriate homology group. Thus the Lefschetz number of the identity map is equal to the alternating sum of the [[Betti number]]s of the space, which in turn is equal to the [[Euler characteristic]] <math>\chi(X)</math>. Thus we have
:<math>\Lambda_{\mathrm{id}} = \chi(X).\ </math>