Periods and Algebraic deRham Cohomology

The prehistory of Algebraic Topology dates back to Euler, Riemann and Betti, who started the idea of attaching various invariants to a topological space. With his simplicial (co)homology theory, Poincaré was the first to give an instance of what in modern terms we would call a contravariant functor H° from the category of (sufficiently nice) topological spaces to the category of cyclic complexes of abelian groups