COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1032

The Complex of Maximal Lattice Free Simplices

Imre Bárány, Roger Howe and Herbert E. Scarf

November 1992

The simplicial complex K(A) is defined to be the collection of simplices, and their proper subsimplices, representing maximal lattice free bodies of the form {x : Ax < b}, with A a fixed (n + 1) × n matrix. The topological space associated with K(A) is shown to be homeomorphic to Rⁿ, and the space obtained by identifying lattice translates of these simplices is homeomorphic to the n-torus.