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 $v_h$ <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content" display="inline"> <mml:mrow> <mml:msub> <mml:mi>v</mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:mrow> </mml:math> -periodic homotopy unless the simplicial complex is a full simplex.