Matthew Stamps: Embedded homotopy sphere arrangements and Orlik-Solomon algebras
Matthew Stamps, KTH
Time: Wed 2014-11-05 10.15 - 11.15
Location: Room 3418, 4th floor, Department of Mathematics, KTH
The Brieskorn and Orlik-Solomon theorems state that the cohomology ring of the complement of a complex hyperplane arrangement is isomorphic to the Orlik-Solomon algebra of its underlying matroid. In this talk, I will show that the homotopy sphere arrangements arising as homotopy colimits of diagrams of spaces on the geometric lattice of a matroid can be embedded into topological spheres when the codimension is greater than equal to two. From this we obtain a Goresky-MacPherson type formula for the cohomology groups of the complements of these arrangements and provide a cohomological interpretation for the Orlik-Solomon algebra of any matroid.