Geodesic
$\Delta$-graphs of polytopes in Bruns and Gubeladze $K$-theory
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 19-24 
M. V. Prikhod'ko. $\Delta$-graphs of polytopes in Bruns and Gubeladze $K$-theory. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 19-24. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a3/
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     title = {$\Delta$-graphs of polytopes in {Bruns} and {Gubeladze} $K$-theory},
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Voir la notice de l'article provenant de la source Math-Net.Ru

W. Bruns and J. Gubeladze introduced a new variant of algebraic $K$-theory, where \linebreak $K$-groups are additionally parametrized by polytopes of some type. In this paper we propose a notion of stable $E$-equivalence which can be used to calculate $K$-groups for high-dimensional polytopes. Polytopes which are stable $E$-equivalent have similar inner structures and isomorphic $K$-groups. In addition, for each polytope we define a $\Delta$-graph which is an oriented graph being invariant under a stable $E$-equivalence.

[1] Bruns W., Gubeladze J., “Polyhedral $K_2$”, Manuscr. Math., 109 (2002), 367–404 | DOI | MR

[2] Bruns W., Gubeladze J., “Higher polyhedral K-groups”, J. Pure and Appl. Algebra, 184 (2003), 175–228 | DOI | MR

[3] Vasershtein L.N., “Osnovy algebraicheskoi K-teorii”, Uspekhi matem. nauk, 31:4(190) (1976) | MR