In this paper, we prove various results on the topology of Grassmannian oriented 3-planes in Euclidean 6-space and compute its cohomology ring. We give self-contained proofs. These spaces come up when studying submanifolds manifolds with calibrated geometries. collect these here for sake completeness. As applications our algebraic topological study present some special Lagrangian-free embedding...
This is an extended account of a short presentation with this title given at the Minneapolis IMA Workshop on ‘n-categories: foundations and applications’, June 7-18, 2004, organised by John Baez and Peter May.
