Related papers: Some examples of aspherical symplectic four-manifo…

This paper has been withdrawn by the author. Lemma 8 is used in the proof of Lemma 6, but it is not correct. Lemma 6 is essential for the main results.

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).

In this paper we construct a minimal symplectic 4-manifold and prove it is homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)

This paper was withdrawn by the author due to an edition's rights

Withdrawn by author due to copyright transfer. See: http://www3.interscience.wiley.com/cgi-bin/abstract/116836954/ABSTRACT

We prove in this paper that any 4-dimensional symplectic manifold is essentially made of finitely many symplectic ellipsoids. The key tool is a singular analogue of Donaldson's symplectic hypersurfaces in irrational symplectic manifolds.

We show that minimal symplectic 4--manifolds with $b_2^+ >1$ and with residually finite fundamental groups are irreducible. We also give examples of irreducible orientable four--manifolds with indefinite intersection forms which are not…

In the paper there are described new examples of conformally flat three dimensional almost cosymplectic manifolds. All these manifolds form a class which was completely characterized.

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

This paper deals with the following question: which manifolds can be realized as leaves of codimension-1 symplectic foliations on closed manifolds? We first observe that leaves of symplectic foliations are necessarily strongly geometrically…

The quantum homology of the monotone complex quadric surface splits into the sum of two fields. We outline a proof of the following statement: The unities of these fields give rise to distinct symplectic quasi-states defined by asymptotic…

This paper shows that the complex projective plane $\mathbb{P}^2$ can be realized as the underlying space for a closed hyperbolic $4$-orbifold. This is the first example of a closed hyperbolic $4$-orbifold whose underlying space is…

Paper withdrawn due to a crucial algebraic error in section 3.

In this paper we show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincare dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question…

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional…

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.

We construct closed, aspherical, smooth 4-manifolds that are homeomorphic but not diffeomorphic. These provide counterexamples to a smooth analog of the Borel conjecture in dimension four. Our technique is to apply the `reflection group…

We analyze the symplectic and complex structures on the panelled web 4-manifolds. In particular, we give infinite family of examples of almost complex but not symplectic and not complex 4-manifolds in the non-simply connected case.

In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.

We show that two orientable, four-dimensional folded symplectic toric manifolds are isomorphic provided that their orbit spaces have trivial degree-two integral cohomology and there exists a diffeomorphism of the orbit spaces (as manifolds…