SIMPLY CONNECTED MANIFOLDS WITH LARGE HOMOTOPY STABLE CLASSES

Abstract For every $k \geq 2$ and $n , we construct n pairwise homotopically inequivalent simply connected, closed $4k$ -dimensional manifolds, all of which are stably diffeomorphic to one another. Each these manifolds has hyperbolic intersection form is parallelisable. In dimension four, exhibit an analogous phenomenon for spin $^{c}$ structures on $S^2 \times S^2$ . $m\geq 1$ also provide similar $(4m-1)$ -connected $8m$ examples, where the number homotopy types in a stable diffeomorphism class related order image J -homomorphism $\pi _{4m-1}(SO) \to \pi ^s_{4m-1}$