Abstract
W. Bruns and J. Gubeladze introduced a new version of algebraic K-theory where K-groups are additionally parameterized by polytopes of some type. In this paper we propose a concept 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 Δ-graph which is an oriented graph being invariant under a stable E-equivalence.
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References
W. Bruns and J. Gubeladze, “Polyhedral K 2,” Manuscr. Math. 109, 367 (2002).
W. Bruns and J. Gubeladze, “Higher Polyhedral K-groups,” J. Pure and Appl. Algebra 184, 175 (2003).
L. N. Vasershtein, “Foundations of Algebraic K-theory,” Uspekhi Matem. Nauk 31(4), 87 (1976) [Russian Math. Surveys 31 (4), 89 (1976)].
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Original Russian Text © M. V. Prikhod’ko, 2013, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2013, Vol. 68, No. 6, pp. 19–24.
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Prikhod’ko, M.V. Δ-graphs of polytopes in Bruns and Gubeladze K-theory. Moscow Univ. Math. Bull. 68, 281–285 (2013). https://doi.org/10.3103/S0027132213060041
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DOI: https://doi.org/10.3103/S0027132213060041