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

Orbit configuration space of standard action and cellular methods of poset