*************************************************************** JOINT TAU-TECHNION SEMINAR ON GEOMETRY & DYNAMICS <http://www.math.tau.ac.il/~ostrover/Seminars/GD/Seminar_GD.html> *************************************************************** TECHNION DATE: Wednesday, March 30, 2011, 13:00 SPEAKER: Egor Shelukhin (Tel-Aviv University) TITLE: Moment maps and quasimorphisms LOCATION: Amado bldg., room 814, Technion ABSTRACT: It has long been known (and is due to many authors) that whenever a group G acts on a Hermitian symmetric space of non-compact type by Kahler isometries, one can construct a bounded two-cocycle on G by integrating the Kahler form over geodesic triangles. Similarly, Reznikov has constructed bounded two-cocycles on groups of symplectomorphisms using their action on the space of compatible almost complex structures. We show that if the action under discussion has an equivariant moment map, such a cocycle has a primitive - a quasimorphism on the universal cover of the group. This holds in the finite-dimensional case - that is for Hermitian Lie groups - giving a reinterpretation of the Guichardet-Wigner quasimorphisms, and for the infinite-dimensional groups of Hamiltonian diffeomorphisms of any finite volume symplectic manifold, generalizing several previous constructions due to Barge-Ghys, Entov and Py. The moment map construction in the second case is due to Donaldson and Fujiki (for the integrable structures). We also compute the restriction of the quasimorphism to the fundamental group and determine its local type. Our construction involves a generalization of Weinstein's Action homomorphism and is related to the Barge-Ghys construction for discrete subgroups of PSL(2,R). --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Michael Entov <entov@math.technion.ac.il>