相关论文: One-sided Heegaard splittings of non-Haken 3-manif…

A Heegaard diagram for a 3-manifold M is a closed, oriented surface S together with a pair (X, Y) of compact 1-manifolds in S whose components serve as attaching curves for the 2-handles of the two sides of a Heegaard splitting for M. The…

This paper has been withdrawn by the author due to a crucial error in the proofs.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

This paper has been withdrawn.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

This paper has been withdrawn by the author(s) and included into the new version of "An extension theorem for separately holomorphic functions with singularities", math.CV/0104089.

In this short note, we give examples of binding sums of contact 3-manifolds that do not preserve properties such as tightness or symplectic fillability. We also prove vanishing of the Heegaard Floer contact invariant for an infinite family…

This paper has been withdrawn by the author due to a new work in [arXiv:0901.0456v4] which can contain the results in this paper.

This paper has been withdrawn by the author due to a crucial error in the Proof of Theorem 0.3

Understanding non-Haken 3-manifolds is central to many current endeavors in 3-manifold topology. We describe some results for closed orientable surfaces in non-Haken manifolds, and extend Fox's theorem for submanifolds of the 3-sphere to…

This paper generalizes the definition of a Heegaard splitting to unify Scharlemann and Thomspon's concept of thin position for 3-manifolds, Gabai's thin position for knots, and Rubinstein's almost normal surface theory. This gives…

In this paper, we prove that (1) For any integers $n\geq 1$ and $g\geq 2$, there is a closed 3-manifold $M_{g}^{n}$ which admits a distance $n$ Heegaard splitting of genus $g$ except that the pair of $(g, n)$ is $(2, 1)$. Furthermore,…

Withdrawn paper because the results are recycled in several other papers and a new definition of T-homotopy is proposed in math.AT/0505152.

This is the fourth of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three…

The equivariant Heegaard genus of a 3-manifold $M$ with the action of a finite group $G$ of diffeomorphisms is the smallest genus of an equivariant Heegaard splitting for $M$. Although a Heegaard splitting of a reducible manifold is…

We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper

The paper referred to in the title is Allard/Almgren 1981 [AA81]. Several months ago Francesco Maggi emailed me saying that the inequalities 5.3(4),(5) of \cite{AA81} were wrong. In fact, as he pointed out, their incorrectness is…

Withdrawn May 2005. There is an error in the even-dimensional case of the proof in the April 2005 version. The hoped-for 4-dimensional applications are unlikely to survive the repairs.

Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_1, V_2; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_i$ are not $\partial$-parallel in $V_i$ for…

This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.

We survey some recent geometric methods for studying Heegaard splittings of 3-manifolds

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.