Reduction of branes in generalized complex geometry

Details Reduction of branes in generalized complex geometry Reduction of branes in generalized complex geometry

2007-01-25

arxiv.org/abs/math/0701740v3

J.Symplectic Geom.6:353-378,2008

Mathematics

Differential Geometry

Final version, to apper in Journal of Symplectic Geometry. Proofs in section 5 simplified. 19 pages

Scientific paper

We show that certain submanifolds of generalized complex manifolds ("weak branes") admit a natural quotient which inherits a generalized complex structure. This is analog to quotienting coisotropic submanifolds of symplectic manifolds. In particular Gualtieri's generalized complex submanifolds ("branes") quotient to space-filling branes. Along the way we perform reductions by foliations (i.e. no group action is involved) for exact Courant algebroids - interpreting the reduced \v{S}evera class - and for Dirac structures.

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