Quotients of the order complex by subgroups of the Young subgroup S1×Sn−1

In this paper we prove that the space is homotopy equivalent to a wedge of spheres of dimension n−3 for all natural numbers n⩾3 and all subgroups G⊂S1×Sn−1. Our argument makes use of Discrete Morse Theory. Furthermore we find a simple formula to compute the number of spheres. For example is homotopy equivalent to a sphere.