Homology of balanced complexes via the Fourier transform

Roy Meshulam

Published 2011-04-25Version 1

Let G_0,...,G_k be finite abelian groups and let G_0*...*G_k be the join of the 0-dimensional complexes G_i. We give a characterization of the integral k-coboundaries of subcomplexes of G_0*...*G_k in terms of the Fourier transform on the group G_0 \times ... \times G_k. This leads to an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.