St. Petersburg Mathematical Journal

Abstract:

The $0$th cohomology group is computed for a complex of groups of cobordism-framed correspondences. In the case of ordinary framed correspondences, an analogous computation was completed by A. Neshitov in his paper “Framed correspondences and the Milnor–Witt $K$-theory”.

Neshitov’s result is, at the same time, a computation of the homotopy groups $\pi _{i,i}(S^0)(Spec(k))$, and the present work might be used subsequently as a basis for computing the homotopy groups $\pi _{i,i}(MGL_{\bullet })(Spec(k))$ of the spectrum $MGL_{\bullet }$.