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

The connection is now explained. 24.58.63.18 ( talk) 19:07, 4 June 2009 (UTC) reply

it would be nice to have a reference (to look up proofs) for the statements about the Frobenius. -- 79.83.77.245 ( talk) 00:49, 19 January 2010 (UTC) reply