Suspension homotopy of 6–manifolds

Abstract

For a simply connected closed orientable manifold of dimension 6, we compute its homotopy decomposition after double suspension. This allows us to determine its Kand KO-groups easily. Moreover, in a special case we refine the decomposition to show the rigidity property of the manifold after double suspension.

Loop homotopy of 6–manifolds over 4–manifolds

“…On the other hand, unstable homotopy theory is a powerful tool for studying the homotopy properties of manifolds preserved by suspending or looping. From the suspension viewpoint, So and Theriault [31] determined the homotopy type of the suspension of connected 4-manifolds, while Huang [19] studied the suspension of simply connected 6-manifolds. From the loop viewpoint, Beben and Theriault [6] studied the loop decompositions of .n 1/-connected 2n-manifolds, while Beben and Wu [8] and Huang and Theriault [20] studied the loop decompositions of the .n 1/-connected .2nC1/-manifolds.…”