Orbit configuration space of standard action and cellular methods of poset

TL;DR

This paper introduces cellular methods for computing homology and cohomology of complex subspace arrangements and orbit configuration spaces, utilizing cellular posets and spectral sequences for advanced algebraic topology analysis.

Contribution

It extends cellular poset concepts, develops new cellular methods for homology computation, and applies these to orbit configuration spaces with spectral sequence tools.

Findings

Presented a cellular approach to intersection lattice homology

Derived a cohomology ring presentation for orbit configuration spaces

Developed a spectral sequence from Grothendieck fibration of posets

Abstract

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.