University of Toronto's Symplectic Geometry Seminar

Monday, 23 March 2009, 2:10pm
BA 6183


University of Toronto

Twisted spin-c structures


Every symplectic manifold carries a distinguished (up to isomorphism) Spin_c-structure, specified by the choice of a compatible almost complex structure. We will generalize this construction to 'morphisms of Dirac structures', viewing symplectic forms as morphisms to the trivial Dirac structure. As an application, we show that all conjugacy classes of a compact Lie group G, and more generally all q-Hamiltonian G-spaces, carry distinguished 'twisted' Spin_c-structures. (Joint work with Anton Alekseev.)