Let $M$ be a closed manifold with holomorphic cell decomposition (if it is complex), or at least with only even cohomology. In particular, its Euler characteristic is equal to the sum of its Betti number.

Let $\phi$ be a diffeomorphism which is isotopic to the identity. As far a I understand, Lefschetz theorem implies that $\phi$ must have at least one fixed point. Moreover, its Lefschetz number is equal to the sum of Betti numbers of $M$.

Is it straightforward then that the number of fixed points of $\phi$, counted with multiplicity, is at least the sum of Betti numbers ? I guess my problem lies in the fact that I don't really know how to relate the Lefschetz number and the multiplicity of the fixed points.