# Arrangements of Submanifolds and the Tangent Bundle Complement

@article{Deshpande2011ArrangementsOS, title={Arrangements of Submanifolds and the Tangent Bundle Complement}, author={Priyavrat Deshpande}, journal={arXiv: Algebraic Topology}, year={2011} }

Drawing parallels with hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection $\mathcal{A}$ of locally flat, codimension-1 submanifolds that intersect like hyperplanes. To such a collection we associate two combinatorial objects: the face category and the intersection poset. We also associate a topological space to the arrangement called the tangent bundle complement. It is the…

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