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JOURNAL OF
ALGEBRAIC
COMBINATORICS
  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Homology of balanced complexes via the Fourier transform

Roy Meshulam

DOI: 10.1007/s10801-011-0315-3

Abstract

Let G 0,\cdots , G k be finite abelian groups, and let G 0\ast  ... \ast  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\ast  ... \ast  G k in terms of the Fourier transform on the group G 0\times  ... \times  G k . This provides a short proof of an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.

Pages: 565–571

Keywords: keywords simplicial homology; Fourier transform

Full Text: PDF

References

1. Björner, A.: Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings.



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