Related papers: Knotted holomorphic discs in C^2

The complement of the codimension 2 complex coordinate subspace arrangement is shown to be homotopy equivalent to a wedge of spheres.

Embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$ are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic…

A non-singular connected algebraic curve $A$ in a simply connected algebraic surface $X$ can be knotted so that its homology class and the fundamental group of its complement in $X$ is preserved, provided $A$ is sufficiently complex (not…

We prove that a proper holomorphic map on the unit disk in the complex plane is uniquely determined up to post-composition with a Moebius transformation by its critical points.

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in the 2-sphere, up to orientation reversion and rotation, and knots with a strong inversion, up to conjugacy. This correspondence…

In this note, we construct a chord index homomorphism from a subgroup of $H_1(\Sigma, \mathbb{Z})$ to the group of chord indices of a knot $K$ in $\Sigma\times I$. Some knot invariants derived from this homomorphism are discussed.

The goal of this paper is the construction of a compact manifold with G$_2$ holonomy and nodal singularities along circles using twisted connected sum method. This paper finds matching building blocks by solving the Calabi conjecture on…

We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a…

We fix a null-homologous, homotopically essential knot $J$ in a 3-manifold with PTFA fundamental group and study concordance of knots that are homotopic to $J$. We construct an infinite family of knots that are characteristic to $J$, and…

We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.

Let $\mathcal {M}$ be the space of all, including singular, long knots in 3-space and for which a fixed projection into the plane is an immersion. Let $cl(\Sigma^{(1)}_{iness})$ be the closure of the union of all singular knots in $\mathcal…

It is shown that a separable exact residually finite dimensional C*-algebra with locally finitely generated (rational) even K-homology embeds in a uniformly hyperfinite C*-algebra.

We prove that for any complex manifold X, the set of all holomorphic maps from the unit disc to X whose images are everywhere dense in X forms a dense subset in the space of all holomorphic maps from the disc to X. We show by an example…

We consider ribbon n-knots for n\geq 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are…

Ng constructed an invariant of knots in ${\mathbb{R}}^3$, a combinatorial knot contact homology. Extending his study, we construct an invariant of surface-knots in ${\mathbb{R}}^4$ using diagrams in ${\mathbb{R}}^3$.

Given a (genus 2) cube-with-holes M, i.e. the complement in S^3 of a handlebody H, we relate intrinsic properties of M (like its cut number) with extrinsic features depending on the way the handlebody H is knotted in S^3. Starting from a…

In the previous paper, the authors constructed a complete holomorphic immersion of the unit disk D into C^2 whose image is bounded. In this paper, we shall prove existence of complete holomorphic null immersions of Riemann surfaces with…

We show that any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m) equipped with a suitable almost-complex structure.

Using spinning we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the…

We prove the existence of embedded closed constant curvature curves on convex surfaces.