12.06.2006 (Monday)

A surgery for generalized complex 4-manifolds

String Theory & Geometry Seminar Gil Cavalcanti (Oxford)

at:
13:30 IC
room Billiard Room, 58 Princes Gate
abstract:

One of the few known obstructions for a 1-connected 4- manifold to admit a symplectic structure is given by Taubes theorem: if b_+ is greater than two, then such a manifold has a nonvanishing Seiberg--Witten invariant. It is only natural to ask whether the same holds for generalized complex manifolds, as introduced by Hitchin, which are a simultaneous generalization of symplectic and complex manifolds. I will introduce a surgery for generalized complex manifolds whose input is a symplectic 4-manifold containing a symplectic 2-torus with trivial normal bundle and whose output is a 4-manifold endowed with a generalized complex structure exhibiting type change along a 2-torus. I will use this surgery to produce an example of a generalized complex manifold with vanishing Seiberg--Witten invariants and hence which does not admit complex or symplectic structures.