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A case study of 𝐴∞-structure

Abstract The computer program Kenzo is used to study complex 𝐴∞-structures coming from iterated loop spaces. The methods of constructive algebraic topology, due to the authors, do produce chain complexes of finite type and chain equivalences with the Hopf algebras canonically associated to the loop spaces. These chain complexes of finite type are therefore endowed with 𝐴∞-structures. It is then experimentally observed, using the Kenzo program, that 𝐴∞-structures of arbitrarily high orders are nontrivial in these objects. This case study is a good illustration of the computing tools given to the topologists by the Kenzo program.