Cobordism-framed correspondences and the Milnor K-theory

Abstract

In this work, we compute the $0$th cohomology group of a complex of groups of cobordism-framed correspondences, and prove the isomorphism to Milnor $K$-groups. An analogous result for common framed correspondences has been proved 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 ${\pi }_{i,i}(S^0)(Spec(k)).$ This work could be used in the future as basis for computing homotopy groups ${\pi }_{i,i}(MG{L}_{\bullet })(Spec(k))$ of the spectrum $MG{L}_{\bullet }.$

arXiv comment18 pages