Related papers: Fibrations of $\mathbb{R}^3$ by oriented lines
Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…
We continue the study of the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, this states that if two Calabi-Yau manifolds X and Y are mirror partners, then X and Y have special Lagrangian torus fibrations which are dual to…
An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts…
For any plane curve singularity defined by an analytic function germ $f$, we construct a spine on each Milnor fiber simultaneously, that realizes the vanishing topology. In order to do so, we study the separatrices at the origin of the…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
In this note we study some analytic properties of the linearized self-duality equations on a family of smooth Riemann surfaces $\Sigma_R$ converging for $R\searrow0$ to a surface $\Sigma_0$ with a finite number of nodes. It is shown that…
A classical two-stranded rope can be made by twisting two identical strands together under strain. Despite being conceptually simple, the contact-equations for helically twisted identical strands have only been solved within the last 20…
This review presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing non-trivial textures, focusing in particular on the common motifs of twisted and…
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…
A Weierstrass fibration is an elliptic fibration $Y\to B$ whose total space $Y$ may be given by a global Weierstrass equation in a $\mathbb{P}^2$-bundle over $B$. In this note, we compute stringy Hirzebruch classes of singular Weierstrass…
We analyse the morphology and kinematics of dense filamentary structures produced in a numerical simulation of a star--forming cloud of $1.4 \times 10^4 \, \Msun$ evolving under their own self--gravity in a magnetized medium. This study is…
We discuss the geometry of the genus one fibrations associated to an elliptic fibration on a K3 surface. We show that the two-torsion subgroup of the Brauer group of a general elliptic fibration is naturally isomorphic to the two-torsion of…
We provide a geometric-combinatorial model for the category of coherent sheaves on the weighted projective line of type (2,2,n) via a cylindrical surface with n marked points on each of its upper and lower boundaries, equipped with an order…
Let $W$ be a nonorientable $4$-dimensional handlebody without $3$- and $4$-handles. We show that $W$ admits a Lefschetz fibration over the $2$-disk, whose regular fiber is a nonorientable surface with nonempty boundary. This is an analogue…
Let $\f: X \ra Z$ be a proper surjective map from a smooth complex manifold $X$ onto a normal variety $Z$. If $\f$ has connected fibers and $-K_X$ is $\f$-ample then $\f$ is called a good contraction. In the present paper we study good…
In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz…
We study the flat CR twistor model $Q^{2,2}\subset \mathbb{CP}^3$ by explicit projective methods. Using the anti-holomorphic involution $j$ associated with the twistor fibration, we classify the projective lines contained in $Q^{2,2}$ into…
Using deformations of foliations to contact structures as well as rigidity properties of Anosov foliations we provide infinite families of examples which show that the space of taut foliations in a given homotopy class of plane fields is in…
We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed…
A symplectic fibration is a fibre bundle in the symplectic category. We find the relation between deformation quantization of the base and the fibre, and the total space. We use the weak coupling form of Guillemin, Lerman, Sternberg and…