Related papers: Structure and classification of torus theta-curves

It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the…

We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser's and Milnor's proof of the existence and uniqueness of the prime decomposition of 3-manifolds. In particular, we do not…

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The…

We study the family of irreducible curves with $\delta$ nodes belonging to a free linear system $|C|$ with smooth general member on a surface $S$ such that $|K_S|$ is ample. Under the assumption that $C$ is numerically equivalent to $pK_S$,…

Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface \Sigma, such that…

In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of…

We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the thrice-punctured torus. As a corollary, we obtain infinitely many commensurability classes…

We describe the invariants of plane quartic curves -- nonhyperelliptic genus 3 curves in their canonical model -- as determined by Dixmier and Ohno, with application to the classification of curves with given structure. In particular, we…

This manuscript introduces a new framework for the study of knots by exploring the neighborhood of knot embeddings in the space of simple open and closed curves in 3-space. The latter gives rise to a knotoid spectrum, which determines the…

We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact…

In this paper, we present a complete coarse classification of non-loose Legendrian and transverse torus knots in any contact structure on $S^1\times S^2$.

We study the topological configurations of the lines of principal curvature, the asymptotic and characteristic curves on a cuspidal edge, in the domain of a parametrization of this surface as well as on the surface itself. Such…

The stable 4-genus of a knot K in 3-space is the limiting value of g_4(nK)/n, where g_4 denotes the 4-genus and n goes to infinity. This induces a seminorm on CQ, the concordance group tensored with the rational numbers. Basic properties of…

Let C be a curve of genus g, and let SU(r) be the moduli space of vector bundles of rank r on C, with trivial determinant. A general E in SU(r) defines a theta divisor in the linear system |r Theta|, where Theta is the canonical theta…

If $X$ is a compact set, a {\it topological contraction} is a self-embedding $f$ such that the intersection of the successive images $f^k(X)$, $k>0$, consists of one point. In dimension 3, we prove that there are smooth topological…

We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular set of the orbit space. As an extension of this work we…

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil…

Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…

In algebraic geometry, trigonal curves can always be embedded into Hirzebruch surfaces. In tropical geometry, the notion of trigonality does not have a unique translation. We focus on the characterization in terms of the existence of a…

We show that any non-minimal bridge decomposition of a torus knot is stabilized and that $n$-bridge decompositions of a torus knot are unique for any integer $n$. This implies that a knot in a bridge position is a torus knot if and only if…