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

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds…

The paper is withdrawn. The proof has an error and it requires a different approach.

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.

The paper is withdrawn because the analysis appeared to be incomplete.

This paper has been withdrawn. Its new version has been published.

In the previous version of the paper it was announced that ``sphere homeomorphic flexible polyhedra (with self intersections) do really exist in n-dimensional Euclidean, Lobachevskij and spherical spaces for each $n\geq 3$.'' Now the paper…

This paper has been withdrawn as the proof of Lemma 4.1 is incomplete.

This paper has been withdrawn by the author due to a crucial error in Lemma 3.5.

This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.

In earlier work, we constructed counterexamples to Lagrangian Poincar\'e recurrence for many toric symplectic four manifolds. Here we provide a few more examples extending the family of counterexamples to include all non-monotone toric…

This paper has been withdrawn by the author due a crucial error.

This paper has been withdrawn by the author, as the proof of Theorem 3.2 contains a flaw; subsequently, both it and Theorem 3.3 are not known to hold. The content of Section 5 has been improved and expanded upon in two separate papers. The…

This paper has been withdrawn by the author due to a gap in the proof of Lemma 3.4

In this paper, Problem 4.17 on R. Kirby's problem list is solved by constructing infinitely many aspherical 4-manifolds that are homology 4-spheres

This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,

We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…

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…

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing…

This paper has been withdrawn by the author due to a crucial error in last part of proof.

Examples of nonformal simply connected symplectic manifolds are constructed.