  We generalise statements known about Springer fibres associated to nilpotents
with 2 Jordan blocks to Spaltenstein varieties. We study the geometry of
generalised irreducible components (i.e. Bialynicki-Birula cells) and their
pairwise intersections. In particular we develop a graphical calculus which
encodes their structure as iterated fibre bundles with CP^1 as base spaces and
compute their cohomology. At the end we present a connection with coloured
cobordisms generalising a construction of Khovanov and Stroppel.
