Higher polyhedral K-groups

Details Higher polyhedral K-groups Higher polyhedral K-groups

2001-08-02

arxiv.org/abs/math/0108013v2

Mathematics

K-Theory and Homology

LaTeX, 51 pp., uses pstricks (including pst-3d)

Scientific paper

We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by polyhedral geometry. This paper is a continuation of [BrG5] (math.KT/0104206) which is devoted to the study of polyhedral aspects of the classical Steinberg relations. The present work explores the polyhedral geometry behind Suslin's well known proof of the coincidence of the classical Volodin's and Quillen's theories. We also determine all K-groups coming from 2-dimensional polytopes.

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