Work

The Goodwillie calculus of polyhedral products

Year: 2026

Type: article

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 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.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2026.10169

Authors: Guy Boyde, Niall Taggart

Institutions: Vrije Universiteit Amsterdam, Queen's University Belfast

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Vrije Universiteit Amsterdam