On a quotient topology of the partition lattice with forbidden block sizes

In this paper we consider subtrisps of Δ ( Π n ) / S 1 × S n − 1 , that we obtain by forbidding certain block sizes, and determine their homotopy type, as well as bases of their cohomology. Our arguments make use of trisp closure maps, which were introduced by Kozlov. A similar result, where Δ ( Π n ) / S n is considered, has already been solved by Kozlov.