  We extend the existing idea of "cellular poset", introduce a collection of
"cellular methods" for the computation of homology of intersection lattice of a
complicated subspace arrangement, and for the computation of multiplicative
structure induced by intersection. As an application, we give a presentation of
cohomology ring of orbit configuration space of standard action by cellular
methods and a spectral sequence associated with Grothendieck fibration of
poset.

Algebraic Topology;Combinatorics