Algebraic topology of G2 manifolds

In this paper we give a survey of various results about the topology of oriented Grassmannian bundles related to the exceptional Lie group G(2). Some of these results are new. We give self-contained proofs here. One often encounters these spaces when studying submanifolds of manifolds with calibrated geometries. For the sake of completeness we decided to collect them here in a self-contained way to be easily accessible for future usage in calibrated geometry. As an application we deduce existence of certain special 3 and 4 dimensional submanifolds of G(2) manifolds with special properties, which appear in the first named author's work with S. Salur about G(2) dualities. (C) 2015 Elsevier GmbH. All rights reserved.