An Explicit Description of Coxeter Homology Complexes. (11th September 2011)

• Record Type: Journal Article
• Authors: Callegaro, Filippo; Gaiffi, Giovanni
• Other Names: Cattaneo A. Academic Editor.; Morozov A. Academic Editor.
• Is Part Of: ISRN geometry. Volume 2011(2011)
• Publication Date: 2011-09-11
• Subjects: Geometry -- Periodicals; Topology -- Periodicals; Geometry; Topology; Periodicals; 516
• DOI: 10.5402/2011/387936
• Languages: English
• ISSNs: 2090-6307

Abstract

Abstract : 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 aboutℤ -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.