Operations on Milnor-Witt K-theory

Abstract

For all positive integers $n$ and all homotopy modules $M_{\ast }$, we define certain operations ${\underline{K}}_n^{\mathrm{MW}}\to M_{\ast }$ and show that these generate the $M_{\ast }(k)$-module of all (in general non-additive) operations ${\underline{K}}_n^{\mathrm{MW}}\to M_{\ast }$ in a suitable sense, if $M_{\ast }$ is $\mathbb{N}$-graded and has a ring structure. This also allows us to explicitly compute the abelian group $\mathrm{Op}({\underline{K}}_n^{\mathrm{MW}},{\underline{K}}_m^{\mathrm{MW}})$ and all operations between related theories such as Milnor, Witt and Milnor-Witt K-theory.

31 pages

References in corpus (3)

• The unit map of the algebraic special linear cobordism spectrum
• Witt and Cohomological Invariants of Witt Classes
• Divided powers in the Witt ring of symmetric bilinear forms