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arXiv · 1812.09979

Cobordism-framed correspondences and the Milnor K-theory

Aleksei Tsybyshev
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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 $\pi_{i,i}(MGL_{\bullet})(Spec(k))$ of the spectrum $MGL_{\bullet}.$

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Aleksei Tsybyshev. 2018-12-24. Cobordism-framed correspondences and the Milnor K-theory. https://arxiv.org/abs/1812.09979

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