Quotients of the topology of the partition lattice which are not homotopy equivalent to wedges of spheres

Ralf Donau

Published 2012-02-20, updated 2012-06-21Version 2

The reader of doi:10.1016/j.topol.2010.08.006 might conjecture that \Delta(\bar{\Pi}_n)/G is homotopy equivalent to a wedge of spheres for any n>=3 and any subgroup G<S_n. We disprove this by showing that \Delta(\bar{\Pi}_p)/C_p is not homotopy equivalent to a wedge of spheres for any prime number p>=5.