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arXiv · 1308.2263

Algebraic topology of $G_2$ manifolds

Selman Akbulut·Mustafa Kalafat
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Abstract

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.

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Selman Akbulut, Mustafa Kalafat. 2013-08-10. Algebraic topology of $G_2$ manifolds. https://doi.org/10.1016/j.exmath.2015.03.004

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