Arrangements of Spheres and Projective Spaces

Details Arrangements of Spheres and Projective Spaces Arrangements of Spheres and Projective Spaces

2012-01-10

arxiv.org/abs/1201.2193v1

Mathematics

Algebraic Topology

Scientific paper

We develop the theory of arrangements of spheres. We consider a finite collection codimension 1 spheres in a given finite dimensional sphere. To such a collection we associate two posets: the face poset and the intersection poset. We also associate a topological space to this collection. The complement of union of tangent bundles of these sub-spheres inside the tangent bundle of the ambient sphere which we call the tangent bundle complement. We find a closed form formula for the homotopy type of this complement and express some of its topological invariants in terms of the associated combinatorial information.

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