Undecidability of the quasi-isomorphism problem for semi-free dg algebras via the cobar construction

2026/05/23 by Manuel Rivera
Mathematics · #math.RA #math.AT

paper · pdf

Abstract

We explain how the undecidability of the quasi-isomorphism and derived Morita equivalence problems for semi-free finitely presented dg associative algebras follows as an immediate consequence of an extension of Adams' cobar theorem to non-simply connected spaces and the triviality problem for finitely presented groups.

Related

• Undecidability problems for semifree DG algebras
• Isomorphism problem and homological properties of DG free algebras
• An elementary approach to the model structure on DG-Lie algebras
• Uncountably many quasi-isometric torsion-free groups
• Unsolvability of the isomorphism problem for [free abelian]-by-free groups