Higher polyhedral K-groups, by Winfried Bruns and Joseph Gubeladze


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 0481 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. Here is a unix shell script that can serve as a netscape helper application for dvi-tar files. This assumes the browser correctly gunzips the file first.
#! /bin/sh
mkdir $TMP
tar xf "$1" -C $TMP || exit 1
(cd $TMP; for i in *.dvi; do xdvi $i; done)
rm -rf $TMP

Winfried Bruns <winfried@mathematik.uni-osnabrueck.de>
Joseph Gubeladze <Joseph.Gubeladze@mathematik.uni-osnabrueck.de>