Speaker : Dr.Ching-Hao Chang (University of Minnesota)
Title : Isotopy of nodal symplectic spheres in rational manifolds
Time : 2013-12-06 (Fri) 16:00 - 17:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: In 1985, M. Gromov proved that any symplectic sphere of degree 1 in is isotopic to an algebraic line. J.Barraud extended Gromov's work to show that any symplectic sphere of degree d in with only positive ordinary double point singularities is symplectically isotopic to an algebraic curve. In this paper, we imitate Barraud's approach and further extend the result to the nodal symplectic spheres in rational manifolds, We prove that if (M, ) is a rational symplectic 4-manifold, and A in (M,Z) a homology class with (A)<0, then , the space of nodal symplectic spheres in the homology class A has only finitely many isotopy classes.