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ISRN Geometry
Volume 2011 (2011), Article ID 387936, 13 pages
Research Article

An Explicit Description of Coxeter Homology Complexes

1Scuola Normale Superiore di Pisa, 56126 Pisa, Italy
2Dipartimento di Matematica, Università di Pisa, 56127 Pisa, Italy

Received 12 May 2011; Accepted 21 June 2011

Academic Editors: A. Cattaneo and A. Morozov

Copyright © 2011 Filippo Callegaro and Giovanni Gaiffi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Rains (2010) computes the integral homology of real De Concini-Procesi models of subspace arrangements, using some homology complexes whose main ingredients are nested sets and building sets of subspaces. We think that it is useful to provide various different descriptions of these complexes, since they encode relevant information about the homotopy type of the models and there still are interesting open questions about -bases of the homology modulo its torsion (see the work by Rains (2010)). In this paper we focus on the case of the Coxeter arrangements: we give an explicit and elementary description, in terms of the combinatorics of the Coxeter groups, of the cells and of the boundary maps of these complexes.