Let \dnk denote the subspace arrangement
formed by all linear subspaces in {\mathbb R}n
given by equations of the form
``ε_1 x_{i_1}=ε_2 x_{i_2}=\dots=
ε_k x_{i_k} 1in}`` where
1\leq i1<\dots k\leq n and
(ε1,\dots, εk) &;{+1,-1}k.
Some important topological properties of such a
subspace arrangement depend on the topology of its
intersection lattice. In previous work on a larger
class of subspace arrangements by Bj"orner & Sagan
BS} the topology of the intersection lattice
{\mathcal L}(\dnk)=\pnkk turned out to be a
particularly interesting and difficult case.
We prove in this paper that \pure(\pnkk) is
shellable, hence that \pnkk is shellable for
k> n}{2}. Moreover we prove that `\widetilde
H_i(\pnkk)=0 unless i\equiv n-2`}
( mod } k-2) or `i\equiv n-3 ( mod
} k-2), and that \widetilde H_i(\pnkk)` is free
abelian for i\equiv n-2 ( mod } k-2). In
the special case of \pkkk we determine homology
completely. Our tools are EC-shellability introduced
in Koz1} and a spectral sequence method for
the computation of poset homology first used in
Han}.
We state implications of our results on the
cohomology of the complement of the considered
arrangements.
