Shuffle products in higher \(K\)-theory
Shuffle products appeared in the Eilenberg-MacLane homology theory of groups. The geometric origin is connected with a systematic simplicial decomposition of a product of simplices. The simplest case arises in the case of a simplicial decomposition of a \(d\)-dimensional torus. The \(\lambda\)-ring structure on the higher \(K\)-theory of a scheme \(X\) is the basic prerequisite to formulate and to prove Riemann-Roch type theorems in higher \(K\)-theory and to define motivic cohomology. The object of this paper is to study the \(\lambda\)-structure not only on the higher \(K\)- group \(K_ q(X)\), but already on the topological space (respectively on the simplicial set) whose homotopy groups are the higher \(K\)-groups. For recent related works, aside from those in the reference section, see, for example: \textit{F. Patras} [C. R. Acad. Sci., Paris, Sér. I 310, 501-504 (1990; Zbl 0695.55014); Bull. Soc. Math. Fr. 119, No. 2, 173-198 (1991; Zbl 0752.55014)], and \textit{R. Morelli} [The \(K\)-theory of a toric variety, Adv. Math. 100, No. 2, 154-182 (1993)].
scientific article; zbMATH DE number 540917
scientific article