Higher polyhedral K-groups

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

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K-Theory and Homology, Algebraic Geometry, Primary 19D06, 19M05; Secondary 14M25, 20G35

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http://salesiana.dossiersoluciones.com/handle/123456789/61955

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108013
 http://arxiv.org/abs/math/0108013

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arXiv