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math.AT2012
Arrangements of Spheres and Projective Spaces
Priyavrat Deshpande
We develop the theory of arrangements of spheres. Consider a finite collection of codimension- subspheres in a positive-dimensional sphere. There are two posets associated with…
math.CO2012
On Arrangements of Pseudohyperplanes
Priyavrat Deshpande
To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completel…