In this paper, usng the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.
Using the degeneration formula for Doanldson-Thomas invariants, we proved formulae for blowing up a point and simple flops.
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
We established a relation between elliptic Gromov-Witten invariants of a symplectic man-ifold M and its blowups along smooth curves and surfaces.
Suppose that two compact manifolds X, X ′ are connected by a sequence of Mukai flops. In this paper, we construct a ring isomorphism between coho-mology ring of X and X ′. Using the localization technique, we prove that the quantum corrected products on X, X ′ are the ordinary intersection products. Furthermore, X, X ′ have isomorphic Ruan cohomology. i.e.… (More)