Related papers: Knotted holomorphic discs in C^2

We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals to assemble colloidal particles trapped at the liquid crystal interface into reconfigurable structures with complex symmetries and packings. Spherical…

We prove that curves of constant torsion satisfy the $C^1$-dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant torsion in each isotopy class. Our methods, which involve convex…

We construct families of quilted surfaces parametrized by the multiplihedra, and define moduli spaces of pseudoholomorphic quilted disks using the theory of pseudoholomorphic quilts of Wehrheim and Woodward. We prove a gluing theorem for…

In this paper, we give an explicit construction of families of $\mathbb{Z}_2$-harmonic 1-forms that degenerate to manifolds with cylindrical ends. We do this by considering certain linear combinations of $L^2$-bounded…

We bound the hyperbolic volumes of a large class of knots and links, called homogeneously adequate knots and links, in terms of their diagrams. To do so, we use the decomposition of these links into ideal polyhedra, developed by Futer,…

Fixing two concordant links in $3$--space, we study the set of all embedded concordances between them, as knotted annuli in $4$--space. When regarded up to surface-concordance or link-homotopy, the set $\mathcal{C}(L)$ of concordances from…

We show that there is an action of the symmetric group on the Hochschild cochain complex of a twisted group algebra with coefficients in a bimodule. This allows us to define the symmetric Hochschild cohomology of twisted group algebras,…

In this paper we construct some invariants of spatial graphs by disk-summing the constituent knots and show the delta edge-homotopy invariance of them. As an application, we show that there exist infinitely many slice spatial embeddings of…

We construct automorphisms of $\C^n$ which map certain discrete sequences one onto another with prescribed finite jet at each point, thus solving a general Mittag-Leffler interpolation problem for automorphisms. Under certain circumstances,…

We prove that Einstein coclosed G_2-structures are nearly parallel.

We describe a general geometrical construction of spherical CR structures. We construct then spherical CR structures on the complement of the figure eight knot and the Whitehead link. They have discrete holonomies contained in $PU(2,1,{\bf…

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.

We consider the ways minimal sets of flows in $S^3$ may be embedded. We prove that given any $C^2$ flow on $S^3$ with positive entropy, there is an uncountable collection $\mathcal{M}$ of topologically distinct minimal sets such that for…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

We give a geometrical demonstration to the existence of holomorphic first integrals for certain kind of vector fields in $\mathbb{C}^2$ and $\mathbb{C}^3$.

This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to study surfaces in larger 4-manifolds. The main results provide a…

We construct a sequence of embedded minimal disks in a ball where the curvatures blow up only at the center. The sequence converges to a limit which is not smooth and not proper.

We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…

We determine all couples of commuting polynomial endomorphisms of C^2 that extends to holomorphic endomorphisms of P^2 and that have disjoint sequences of iterates.