Talk:Lefschetz fixed-point theorem

Lefschetz number

is defined arbitrarily for maps $X\rightarrow X$, then if we use the identity map we get $\Lambda _{id}=\#(\Delta ,\Delta ,M\times M)=\chi (M)$ is the intersection number of the diagonal with itself in the product manifold $M\times M$, i.e., the Euler characteristic. On the algebraic topological level I'm sure this holds too, that $\chi (M)=\Lambda _{id}(M)$. Anyone know more about this? MotherFunctor 05:55, 28 May 2006 (UTC)