Chennai Mathematical Institute


3.30 pm, Seminar Hall
The Goresky-MacPherson formula for topic arrangements

Priyavrat Deshpande
Chennai Mathematical Institute.


An arrangement of subspaces is a finite collection of subspaces in an Euclidean space. As an application of their 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. This work generated a lot of activity; several applications, reproofs, an etale analogue etc. 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.