The Coalgebra of Chains and the Fundamental Group

I will explain the sense in which the natural algebraic structure of the singular chains on a path-connected space determines its fundamental group. This is a conceptual observation which has several important consequences, one of them being the following extension of a classical theorem of Whitehead: a continuous map between path-connected pointed spaces is a weak homotopy equivalence if and only if the induced map between the differential graded coalgebras of singular chains is a cobar-quasi-isomorphism (i.e. a quasi-isomorphism after applying the cobar functor). Another consequence is the following statement over a field F of arbitrary characteristic: two path-connected pointed spaces X and Y are connected by a zig-zag of maps inducing isomorphisms on fundamental groups and on homology with coefficients in any local system if and only if the simplicial cocommutative coalgebras of chains FX and FY are cobar-quasi-isomorphic.
The main ingredients needed to formulate and prove these results are: 1) an extension of a classical theorem of Adams which relates the cobar construction to the based loop space of any path-connected space 2) the symmetry of the diagonal map and its chain approximations, and 3) a theorem of P. Goerss relating Bousfield localization and the simplicial coalgebra of chains.