Homotopy groups of certain highly connected manifolds via loop space homology
Osaka Journal of Mathematics
For n ≥ 2 we consider (n − 1)-connected closed manifolds of dimension at most (3n − 2). We prove that away from a finite set of primes, the p-local homotopy groups of M are determined by the dimension of the space of indecomposable elements in the cohomology ring H∗(M;Q). Moreover, we show that these p-local homotopy groups can be expressed as a direct sum of p-local homotopy groups of spheres. This generalizes some of the results of our earlier work .
Basu, Samik and Basu, Somnath, "Homotopy groups of certain highly connected manifolds via loop space homology" (2019). Journal Articles. 888.