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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

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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.