  We study in detail two row Springer fibres of even orthogonal type from an
algebraic as well as topological point of view. We show that the irreducible
components and their pairwise intersections are iterated P^1-bundles. Using
results of Kumar and Procesi we compute the cohomology ring with its action of
the Weyl group. The main tool is a type D diagram calculus labelling the
irreducible components in an convenient way which relates to a diagrammatical
algebra describing the category of perverse sheaves on isotropic Grassmannians
based on work of Braden. The diagram calculus generalizes Khovanov's arc
algebra to the type D setting and should be seen as setting the framework for
generalizing well-known connections of these algebras in type A to other types.
The results will be connected to Brauer algebras at non-generic parameters in a
subsequent paper.
