Manifold arrangements

TL;DR

This paper extends the computation of the cd-index to more general manifold arrangements, including various manifolds and stratifications, broadening the scope of previous results in geometric combinatorics.

Contribution

It generalizes the calculation of the cd-index to arrangements on diverse manifolds, not limited to spheres or tori, and allows for submanifolds of arbitrary codimension.

Findings

Derived the cd-index for arrangements on general manifolds.

Extended previous results to Whitney stratifications.

Included submanifolds of arbitrary codimension.

Abstract

We determine the cd-index of the induced subdivision arising from a manifold arrangement. This generalizes earlier results in several directions: (i) One can work with manifolds other than the n-sphere and n-torus, (ii) the induced subdivision is a Whitney stratification, and (iii) the submanifolds in the arrangement are no longer required to be codimension one.