On the Euler–Poincaré characteristics of a simply connected rationally elliptic CW-complex

Abstract

For a simply connected rationally elliptic CW-complex X, we show that the cohomology and the homotopy Euler–Poincaré characteristics are related to two new numerical invariants namely $$\eta _{X}$$ and $$\rho _{X}$$ which we define using the Whitehead exact sequences of the Quillen and the Sullivan models of X.