Suspension homotopy of $6$-manifolds

Abstract

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

19 pages; comments are welcome

References in corpus (1)

• Loop space decompositions of $(2n-2)$-connected $(4n-1)$-dimensional Poincaré Duality complexes

Cited by in corpus (2)

• Loop homotopy of $6$-manifolds over $4$-manifolds
• The homotopy type of a once-suspended 6-manifold and its applications