The Goodwillie calculus of polyhedral products

2024/02/12 by Guy Boyde, Boyde, Guy, Niall Taggart +1
Mathematics · #18F50 #55P60 #57S12 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2402.07774

Abstract

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 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 v_h-periodic homotopy unless the simplicial complex is a full simplex.

Citations

• Partition Complexes, Tits Buildings and Symmetric Products
• The homology of certain subgroups of the symmetric group with coefficients in Lie(n)

Related

• Polyhedral products and features of their homotopy theory
• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces
• A spectral sequence for polyhedral products
• Polyhedral products in abstract and motivic homotopy theory
• Polyhedral coproducts