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The Goresky-MacPherson formula for toric arrangements

  • Priyavrat Deshpande, CMI Chennai

An arrangement of subspaces is a finite collection of subspaces
in an Euclidean space. As an application of stratified Morse theory, Goresky
and MacPherson gave a formula for the cohomology of the complement of
a subspace arrangement in terms of the homology of lower intervals of an
associated semi-lattice. In this talk I will consider toric arrangements, i.e., finite
collection of codimension 1 subtori in a torus. Using Vassiliev's simplicial
resolution and a spectral sequence argument prove the analogue of
Goresky-MacPherson formula in this context.