The Goodwillie calculus of polyhedral products

We describe the Goodwillie calculus of polyhedral products in the case that the fat wedge filtration on the associated real moment-angle complex is trivial. We do this by analysing the behaviour on the calculus of the Denham–Suciu fibre sequence, the Iriye–Kishimoto decomposition of the polyhedral product constructed from a collection of pairs of cones and their bases, and the Hilton–Milnor decomposition. As a corollary, we show that the Goodwillie calculus of these polyhedral products converges integrally and diverges in vh $v_h$ v h -periodic homotopy unless the simplicial complex is a full simplex.