Related papers: Some examples of aspherical symplectic four-manifo…
Withdrawn due to an incompleteness of the main results.
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
This paper is withdrawn. We found a mistake in Lemma 4.1
This short paper shows a topological obstruction of the existence of certain Lagrangian submanifolds in symplectic $4m$-manifolds.
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
This paper is being withdrawn because an error was discovered in lemma 4.3. Although the rest of the paper appears to be correct, this error invalidates the proof of theorem 3.1 and theorem 3.3.
The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.
This paper has been withdrawn by the author due to incomplete interpretation for the results.
We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.
This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.
Paper withdrawn. Error lemma 7.
This paper has been withdrawn by the author because there is a gap in Lemma 9.
This paper has been withdrawn by the author due to a crucial error in the proofs. The error has been corrected and the paper has been expanded in arXiv:0910.5327
Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!
The paper is withdrawn due to some errors.
This paper has been withdrawn by the author due to a mistake in the section 4.
The content of this unpublished paper is subsumed in successive work of the authors, in particular arXiv:1102.0820, arXiv:1102.0821 and arXiv:1205.2434.
The paper was withdrawn because of its significant overlap with a paper appeared recently.
We prove the vanishing of many Welschinger invariants of real symplectic $4$-manifolds. In some particular instances, we also determine their sign and show that they are divisible by a large power of 2. Those results are a consequence of…
This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.