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arXiv · 1608.08949

Gerbes on $G_2$ Manifolds

Goncalo Oliveira
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Abstract

On a projective complex manifold, the Abelian group of Divisors maps surjectively onto that of holomorphic line bundles (the Picard group). On a $G_2$-manifold we use coassociative submanifolds to define an analogue of the first, and a gauge theoretical equation for a connection on a gerbe to define an analogue of the last. Finally, we construct a map from the former to the later. Finally, we construct some coassociative submanifolds in twisted connected sum $G_2$-manifolds.

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Goncalo Oliveira. 2016-08-31. Gerbes on $G_2$ Manifolds. https://doi.org/10.1016/j.geomphys.2017.01.007

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