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

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.

Fixed typos and added a reference to the "K3 Problem List". To appear in Math. Proc. Camb. Phil. Soc