Geometrically constructed bases for homology of non-crossing partition lattices (Q1028825)

Summary: For any finite, real reflection group \(W\), we construct a geometric basis for the homology of the corresponding non-crossing partition lattice. We relate this to the basis for the homology of the corresponding intersection lattice introduced by \textit{A. Björner} and \textit{M. L. Wachs} [Electron. J. Comb. 11, No. 2, Research paper R3, 26 p. (2004; Zbl 1064.05151)] using a general construction of a generic affine hyperplane for the central hyperplane arrangement defined by \(W\).