Suspension homotopy of $6$-manifolds

TL;DR

This paper investigates the homotopy decomposition of simply connected closed orientable 6-manifolds after double suspension, enabling easier computation of their K-theory groups and revealing rigidity properties in special cases.

Contribution

It provides a homotopy decomposition result for 6-manifolds after double suspension and refines this to demonstrate rigidity in certain cases, advancing understanding of their topological structure.

Findings

Homotopy decomposition after double suspension for 6-manifolds

Simplified computation of K- and KO-groups

Rigidity property established in a special case

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.