Gerbes on G2 manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:114

Article

Oliveira, Goncalo¹ 

[1] Duke Univ, Durham, NC 27706 USA

关键词: G2 manifold;    Gerbe;    Coassociative Submanifold;   

DOI  :  10.1016/j.geomphys.2017.01.007

来源: Elsevier

【 摘 要 】

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 divisors, and a gauge theoretical equation for a connection on a gerbe to define an analogue of the Picard group. Then, we construct a map from the former to the later. We also prove that the canonical map from our analogue of the Picard group to the third cohomology group with integer coefficients is surjective. AS a side remark we make an observation relating the topological type of coassociative submanifolds and the cohomology classes they represent. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free