On the Betti number of the space of invariant paths on the space whose cohomology is the exterior algebra with two generators
Let \(M\) a Riemannian closed manifold whose \(\text{mod 2}\) cohomology algebra is isomorphic to that of the product of two spheres with different dimensions. Using the Cobar type Eilenberg-Moore spectral sequence, the author proves that every isometry on \(M\) has infinitely many invariant geodesics. This result is obtained from a good characterization for the boundeness of rational Betti numbers of the space of invariant paths in \(M\).
cobar type Eilenberg-Moore spectral sequences
scientific article; zbMATH DE number 1879116