• Corpus ID: 117339994

Arrangements of Submanifolds and the Tangent Bundle Complement

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