Spaces whose rational homology and de Rham homotopy are both finite dimensional.(English)Zbl 0546.55015

Homotopie algébrique et algèbre locale, Journ. Luminy/France 1982, Astérisque 113-114 (1984).
Summary: [For the entire collection see Zbl 0535.00017.]
If a simply connected space S satisfies the hypothese of the title let n be the top integer for which $$H^ n(S;{\mathbb{Q}})\neq 0.$$ It was known that $$\sum^{2n-1}_{i=n+1}\dim \pi_ i(S)\otimes {\mathbb{Q}}\leq 1;$$ the case when equality holds is analyzed. We also show that $$\dim H^*(S;{\mathbb{Q}})\leq 2^ n,$$ and derive a formula for the Lefschetz number of a map.

MSC:

 55P62 Rational homotopy theory 55M20 Fixed points and coincidences in algebraic topology

Zbl 0535.00017