Lefschetz principle

Loose statement
Let $$H$$ be a cohomology theory, and $$g$$ be an endomorphism of a space $$X$$. Then, under under appropriate circumstances:

$$\sum_{i \ge 0} (-1)^i tr(g,H^i(X)) = \chi_E(X^g)$$

Here, $$\chi_E$$ is the Euler characteristic, defined as follows:

$$\chi_E(Y) = \sum_{i \ge 0} (-1)^i dim H^i(Y)$$

Here $$X^g$$ denotes the set of those points in $$X$$ that are fixed under the action of $$g$$.

Relation with other principles

 * Hopf principle