Related papers: On certain exotic 4-manifolds of Akhmedov and Park

Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…

In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-K\"{a}hler Calabi-Yau 6-manifolds with…

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some…

In this short article we give a criterion whether a given minimal symplectic 4-manifold with $b_{2}^{+}=1$ having a torsion-free canonical class is rational or ruled. As a corollary, we confirm that most of homotopy elliptic surfaces…

Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,\omega)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the…

By applying the lantern relation substitutions to the positive relation of the genus two Lefschetz fibration over $\mathbb{S}^{2}$. We show that $K3\#2 \overline{\mathbb{CP}}{}^{2}$ can be rationally blown down along seven disjoint copies…

We construct a uniformly bounded symplectic structure on $S^2 \times \mathbb{R}^4$ admitting embeddings by arbitrarily large balls. This provides a counterexample to a recent conjecture of Savelyev. We then prove the conjecture holds for a…

We introduce the notion of symplectic flatness for connections and fiber bundles over symplectic manifolds. Given an $A_\infty$-algebra, we present a flatness condition that enables the twisting of the differential complex associated with…

Given a symplectomorphism f of a symplectic manifold X, one can form the `symplectic mapping cylinder' $X_f = (X \times R \times S^1)/Z$ where the Z action is generated by $(x,s,t)\mapsto (f(x),s+1,t)$. In this paper we compute the Gromov…

We shall give an example of irreducible symplectic manifolds X and Y which are not bimeromorphic, but have the same periods in the second cohomologies. More explicitly, X and Y are generalized Kummer varieties of dim 4 for a general complex…

This paper concerns different types of singular complex projective varieties generalizing irreducible symplectic manifolds. We deduce from known results that the generalized Beauville-Bogomolov form satisfies the Fujiki relations and has…

Kreck and Schafer produced the first examples of stably diffeomorphic closed smooth 4-manifolds which are not homotopy equivalent. They were constructed by applying the doubling construction to 2-complexes over certain finite abelian groups…

We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can…

We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements,…

A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.

In an earlier paper we explained how to convert the problem of symplectically embedding one 4-dimensional ellipsoid into another into the problem of embedding a certain set of disjoint balls into \CP^2 by using a new way to desingularize…

We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral…

The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified…

We construct invariants under deformation of real symplectic 4-manifolds. These invariants are obtained by counting three different kinds of real rational J-holomorphic curves which realize a given homology class and pass through a given…

We construct a new family {K_n} of simply connected symplectic 4-manifolds with the property c_1^2(K_n)/chi(K_n) -> 9 (as n goes to infinity).