Deformations of G2-structures with torsion - Sergey Grigorian (Stony Brook)

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Date: Thursday 26th January 2012Speaker: Sergey Grigorian (Stony Brook).Title: Deformations of G2-structures with torsion.Abstract: We consider non-infinitesimal deformations of G2-structures on 7-dimensional manifolds and derive a closed expression for the torsion of the deformed G2-structure. We then specialize to the case where the deformation liesin the seven-dimensional representation of G2 and is hence defined by a vector v. In this case, we explicitly derive the expressions for the different torsion components ofthe new G2-structure in terms of the old torsion components and derivatives of v. In particular this gives a set of differential equations for the vector v which have to be satisfied for a transition between G2-structures with particular torsions. For some specific torsion classes we then explore the solutions of these equations.http://www.maths.ed.ac.uk/cheltsov/seminar/