Related papers: Khovanov's invariant for closed surfaces

We consider the problem of the persistence of invariant curves for analytical fibered holomorphic transformations. We define a fibered rotation number associated to an invariant curve. We show that an invariant curve with a prescribed…

We relate the Donaldson invariants of two four-manifolds $X_i$ with embedded Riemann surfaces of genus 2 and self-intersection zero with the invariants of the manifold X which appears as a connected sum along the surfaces. When the original…

If a finite group of orientation-preserving diffeomorphisms of the 3-dimensional torus leaves invariant an oriented, closed, embedded surface of genus g>1 and preserves the orientation of the surface, then its order is bounded from above by…

This paper studies smooth obstructions to integrability and proves two main results. First, it is shown that if a smooth topological n-torus admits a real-analytically completely integrable convex hamiltonian on its cotangent bundle, then…

We construct three sequences of regular surfaces of general type with unbounded numerical invariants whose canonical map is 2-to-1 onto a canonically embedded surface. Only sporadic examples of surfaces with these properties were previously…

A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology. We show that if a knot $K$ has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all…

We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3…

We consider surface links in the 4-space which are presented by the form of simple branched coverings over the standard torus, which we call torus-covering links. In this paper, we study unknotting numbers of torus-covering links. In some…

Open Gromov-Witten invariants in general are not well-defined. We discuss in detail the enumerative numbers of the Clifford torus $T^2$ in $\CP^2$. For cyclic A-infinity algebras, we show that certain generalized way of counting may be…

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian…

Updated rerefences and introduction. Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we…

A problem about Khovanov homology and 3-manifolds is discussed in this paper.

First we characterize all the polynomial vector fields in $\R^4$ which have the Clifford torus as an invariant surface. After we study the number of invariant meridians and parallels that such polynomial vector fields can have in function…

This is the third in our series of papers relating gauge theoretic invariants of certain 4-manifolds with invariants of 3-manifolds derived from Rohlin's theorem. Such relations are well-known in dimension three, starting with Casson's…

Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according…

In previous work we introduced a Khovanov multicurve invariant $\operatorname{\widetilde{Kh}}$ associated with Conway tangles. Applying ideas from homological mirror symmetry we show that $\operatorname{\widetilde{Kh}}$ is subject to strong…

We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These…

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily…

We show that for any closed, orientable surface $K$ smoothly embedded in $\mathbb{R}^4$, the unit $4$-ball $B^4 \subset \mathbb{R}^4$ can be tiled using $n \geq 3$ tiles each congruent to a regular neighborhood (with corners) of a surface…

We obtain an equivariant classification for orientable, closed, four-dimensional Alexandrov spaces admitting an isometric torus action. This generalizes the equivariant classification of Orlik and Raymond of closed four-dimensional…