W. Bruns, J. Gubeladze
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.
Lattice polytopes, semigroup rings, automorphism groups, Milnor's group, Volodin's theory, + construction.
MSC 2000: 14M25, 19C09, 19D06, 19M05, 52B20