The homotopy type of a once-suspended 6-manifold and its applications

TL;DR

This paper provides a homotopy decomposition of the suspension of certain 6-manifolds, enabling calculations of cohomology groups and homotopy types of gauge groups over these manifolds.

Contribution

It introduces a homotopy decomposition of the suspension of simply connected 6-manifolds after localization away from 2, facilitating new computations in topology.

Findings

Homotopy decomposition of suspended 6-manifolds into spheres and Moore spaces

Calculation of generalized cohomology groups for these manifolds

Determination of homotopy types of gauge groups over the manifolds

Abstract

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate generalized cohomology groups of $M$ and determine the homotopy types of gauge groups of certain bundles over $M$.