Symplectic 4-manifolds with arbitrary fundamental group near the Bogomolov-Miyaoka-Yau line

Is there a topological Bogomolov--Miyaoka--Yau inequality?

The aim of this paper is to consider a possible extension of the Bogomolov--Miyaoka--Yau inequality to differentiable orbifolds. The conjectured extension is related to the Montgomery--Yang problem about circle actions on the 5--sphere and also to the H--cobordism of Seifert fibered 3--manifolds. Related conjectures on algebraic surfaces with quotient singularities which have the same rational homology as the projective plane are also considered. Finally we give such examples which are birational to the projective plane yet have ample canonical class.

自旋辛4-流形的几何问题的斜率不等式

Slope Inequalities for the Geography Problem of Spin Symplectic 4-Manifolds

该研究基于Roulleau与Urzúa的复曲面成果，构造了自旋辛4-流形的无限多互不同胚光滑结构，并指出其结果接近辛Bogomolov-Miyaoka-Yau不等式给出的最优边界。

Note on new symplectic 4-manifolds with nonnegative signature

In this short note, we present a construction of new symplectic 4-manifolds with non-negative signature using the complex surfaces on Bogomolov-Miyaoka-Yau line $c_1^2 = 9χ_h$, the fake projective planes and Cartwright-Steger surfaces. Our construction yields an infinite family of fake rational homology $(2n-1)\CP#(2n-1)\CPb$ for any integer $3 \leq n \leq 22$.

几何可分解的非球面4流形的符号差

The signature of geometrically decomposable aspherical 4-manifolds

本文构造了具有非零符号差的几何可分解非球面4流形，证明其满足Bogomolov--Miyaoka--Yau型不等式，并给出达到等号的非几何例子及更高图4流形中严格不等式的无穷多实例。

模空间上几乎正交结构及对辛四维流形拓扑的应用

Almost Hermitian structures on moduli spaces of non-Abelian monopoles and applications to the topology of symplectic four-manifolds

本文通过Morse理论研究非阿贝尔单极模空间的几乎正交结构，证明了辛四维流形上Bogomolov-Miyaoka-Yau不等式成立。

On the geography of simply connected nonspin symplectic $4$-manifolds with nonnegative signature

In \cite{AP3, AHP}, the first author and his collaborators constructed the irreducible symplectic $4$-manifolds that are homeomorphic but not diffeomorphic to $(2n-1){\mathbb{CP}}^{2}\#(2n-1)\overline{\mathbb{CP}}^{2}$ for each integer $n \geq 25$, and the families of simply connected irreducible nonspin symplectic $4$-manifolds with positive signature that are interesting with respect to the symplectic geography problem. In this paper, we improve the main results in \cite{AP3, AHP}. In particular, we construct (i) an infinitely many irreducible symplectic and non-symplectic $4$-manifolds that…