Symplectic 4-Manifolds on the Noether Line and between the Noether and Half Noether Lines

Rational surfaces and symplectic 4-manifolds with one basic class

We present constructions of simply connected symplectic 4-manifolds which have (up to sign) one basic class and which fill up the geographical region between the half-Noether and Noether lines.

Symplectic embeddings of four-dimensional polydisks into half integer ellipsoids

We obtain new sharp obstructions to symplectic embeddings of four-dimensional polydisks $P(a,1)$ into four-dimensional ellipsoids $E(bc,c)$ when $1\le a< 2$ and $b$ is a half-integer. When $1 \leq a < 2-O(b^{-1})$ we demonstrate that $P(a,1)$ symplectically embeds into $E(bc,c)$ if and only if $a+b\le bc$. Our results show that inclusion is optimal and extend the result by Hutchings \cite{H} when $b$ is an integer. Our proof is based on a combinatorial criterion developed by Hutchings \cite{H} to obstruct symplectic embeddings.

Stabilized convex symplectic manifolds are Weinstein

We show that a stabilized convex symplectic (also called Liouville) manifold with the homotopy type of a half dimensional CW-complex is symplectomorphic to a flexible Weinstein manifold.

带边接触不变量与半 Giroux 挠率

Bordered contact invariants and half Giroux torsion

本文利用带边接触不变量和纽结补的最内层接触结构，构造沿分离环面含半 Giroux 挠率但接触不变量非零的无穷多闭接触3维流形，反驳 Ghiggini 猜想并确定 2π 为使不变量消失的最小扭转量。