Geometry with torsion and multi-moment maps

Geometry with torsion and multi-moment maps

Thu, 10/06/2010
12:00 		Thomas Bruun Madsen (Odense) Junior Geometry and Topology Seminar Add to calendar SR1
Geometry with torsion and multi-moment maps
On any Hermitian manifold there is a unique Hermitian connection, called the Bismut connection, which has torsion a three-form. One says that the triplet consisting of the Hermitian structure together with the Bismut connection specifies a Kähler-with-torsion structure, or briefly a KT structure. If the torsion three-form is closed, we have a strong KT structure. The first part of this talk will discuss these notions and also address the problem of classifying strong KT structures.

Despite their name, KT manifolds are generally not Kähler. In particular the fundamental two-form is not closed. If the KT structure is strong, we have instead a closed three-form. Motivated by the usefulness of moment maps in geometries involving symplectic forms, one may ask whether it is possible to construct a similar type of map, when we replace the symplectic form by a closed three-form. The second part of the talk will explain the construction of such maps, which are called multi-moment maps.