相关论文: Examples of symplectic 4-manifolds with positive s…

In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points $(\chi, c)$ lying in $0 \leq c \leq 8.76\chi$. Furthermore, as a corollary, we prove…

Symplectic 4-manifolds $(X,\omega)$ with $b_+{=}1$ are roughly classified by the canonical class $K$ and the symplectic form $\omega$ depending upon the sign of $K^2$ and $K\cdot \omega$. Examples are known for each category except for the…

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 $c_1^2 = 9\chi_h$, the fake projective planes and Cartwright-Steger surfaces.…

In this paper we construct a family of symplectic 4--manifolds with positive signature for any given fundamental group $G$ that approaches the BMY line. The family is used to show that one cannot hope to do better than than the BMY…

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…

We produce infinitely many distinct irreducible smooth 4-manifolds homeomorphic to #(2m+1)(CP^2 # -CP^2) and #(2n+1)(S^2 x S^2), respectively, for each m>3 and n>4. These provide the smallest exotic closed simply connected 4-manifolds with…

We present the various constructions of new symplectic $4$-manifolds with non-negative signatures using the complex surfaces on the BMY line $c_1^2 = 9\chi_h$, the Cartwright-Steger surfaces, the quotients of Hirzebruch's certain…

We construct examples of simply connected nonalgebraic symplectic fourfolds with a prescribed number of nonintersecting symplectic curves with positive self-intersections.

We construct an infinite family of simply connected, pairwise nondiffeomorphic 4-manifolds, all homeomorphic to 3CP^2 blown up at 9 points.

In this article, we present new symplectic 4-manifolds with same integral cohomology as $S^{2}\times S^{2}$. The generalization of this construction is given as well, an infinite family of symplectic 4-manifolds cohomology equivalent to…

In this article we construct a new family of simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a…

For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$, $\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic $e$ and…

It is the purpose of this paper to construct families of examples of nonsymplectic 4-manifolds which (up to sign) have just one Seiberg-Witten basic class.

We prove that a positive definite smooth four-manifold with $b_2^+ \geq 2$ and having either no 1-handles or no 3-handles cannot admit a symplectic structure.

The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain…

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, and any real second cohomology class of positive square is…

Let $M$ be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer $n\geq 3$. We construct an irreducible symplectic 4-manifold homeomorphic to $M$ and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic…

This article has two parts. In the first part we introduce two positivity conditions for the modified $\chi_y$-genus on almost-complex manifolds and show that each of them implies a family of optimal Chern number inequalities. It turns out…

We construct an infinite family of homologous, non-isotopic, symplectic surfaces of any genus greater than one in a certain class of closed, simply connected, symplectic four-manifolds. Our construction is the first example of this…

For every integer $k\geq 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and $(2k-1)(\CP#\CPb)$, the connected sums of $2k-1$ copies of…