**W. Bruns, J. Gubeladze**

## Polytopes and K-theory

**Abstract:**

This is an overview of results from our experiment of merging
two seemingly unrelated disciplines -- higher algebraic K-theory of rings and
the theory of lattice polytopes. The usual K-theory is the "theory of a unit
simplex". A conjecture is proposed on the structure of higher polyhedral
K-groups for certain class of polytopes for which the coincidence of Quillen's
and Volodin's theories is known.

**Keywords:**

Lattice polytopes, semigroup rings, automorphism groups, Milnor's group,
Volodin's theory, + construction.

**MSC 2000:** 14M25, 19C09, 19D06, 19M05, 52B20