6 papers
Symplectic Parshin-Arakelov inequality
Tian-Jun Li
Lefschetz fibration is the symplectic analogue of stable holomorphic fibration in complex geometry. A 4-dimensional stable holomorphic fibration satisfies the famous Parshin-Arakel…
Symplectic genus, minimal genus and diffeomorphisms
Bang-He Li, Tian-Jun Li
In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied.…
Family Seiberg-Witten invariants and wall crossing formulas
Tian-Jun Li, Ai-Ko Liu
In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surfa…
Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4-manifolds with b^+=1
Tian-Jun Li, Ai-Ko Liu
Let M be a closed oriented smooth 4-manifold admitting symplectic structures. If M is minimal and has b^+=1, we prove that there is a unique symplectic canonical class up to sign,…
An example concerning Ohtsuki's invariant and the full SO(3) quautum invariant
Bang-He Li, Tian-Jun Li
Two lens spaces are given to show that Ohtsuki's for rational homology spheres does not determine Kirby-Melvin's
Kirby-Melvin's and Ohtsuki's for Lens spaces
Bang-He Li, Tian-Jun Li
In this note, we first derive explicit formulas for Kirby-Melvin's three-manifold invariants for all Lens spaces from our results for another set of invariants defi…