Graham Ellis, James Harris, Emil Skldberg
Polytopal resolutions for finite groups
For a finite group G acting faithfully on euclidean space we consider the convex hull of the orbit of a suitable vector. We show that the combinatorial structure of this polytope determines a polynomial growth free ℤG-resolution of ℤ. A resolution due to De Concini and Salvetti is recovered when G is a finite reflection group. A resolution based on the simplex is obtained from the regular representation of a finite group. □
Our aim in this paper is to explain how, for any finite group G, a finite calculation involving convex hulls leads to an explicit recursive description of all dimensions of a free ℤG-resolution in which the number of generators grows polynomially with dimension.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2006, 09/2006
Pages: 131 - 137
Show full article (external site)
Show all available items of this journal
Search
