### 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
TMP=/tmp/play-$$
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>