Related papers: Lamination links in 3-manifolds

The total space of the tangent bundle of a K\"ahler manifold admits a canonical K\"ahler structure. Parallel translation identifies the space ${\Bbb{T}}$ of oriented affine lines in ${\Bbb{R}}^3$ with the tangent bundle of $S^2$. Thus, the…

For a compact connected 3-submanifold with connected boundary in the 3-sphere, we relate the existence of a Seifert surface system for a surface with a Dehn surgery along a null-homologous link. As its corollary, we obtain a refinement of…

We show that a group presented by a labelled oriented tree presentation in which the tree has diameter at most three is an HNN extension of a finitely presented group. From results of Silver, it then follows that the corresponding higher…

We study associative submanifolds of the Berger space SO(5)/SO(3) endowed with its homogeneous nearly-parallel G2-structure. We focus on two geometrically interesting classes: the ruled associatives, and the associatives with special Gauss…

We show that three natural decision problems about links and 3-manifolds are computationally hard, assuming some conjectures in complexity theory. The first problem is determining whether a link in the 3-sphere bounds a Seifert surface with…

We establish the existence of a non-trivial, branched immersion of a closed Riemann surface $\Sigma$ with constant mean curvature (CMC) $H$ into any closed, orientable 3-manifold $\mathcal{M}$, for almost every prescribed value of $H$. The…

Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of such manifolds. In…

We show that every auto-homeomorphism of the unmeasured lamination space of an orientable surface of finite type is induced by a unique extended mapping class unless the surface is a sphere with at most four punctures or a torus with at…

Classical fully augmented links have explicit hyperbolic geometry, and have diagrams on the 2-sphere in the 3-sphere. We generalise to construct fully augmented links projected to the reflection surface of any 3-manifold obtained by…

We give an example of a 3-component smoothly slice boundary link, each of whose components has a genus one Seifert surface, such that any metaboliser of the boundary link Seifert form is represented by 3 curves on the Seifert surfaces that…

We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…

We consider hyperbolic links that admit alternating projections on surfaces in compact, irreducible 3-manifolds. We show that, under some mild hypotheses, the volume of the complement of such a link is bounded below in terms of a Kauffman…

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend…

In this survey paper we present results about link diagrams in Seifert manifolds using arrow diagrams, starting with link diagrams in $F\times S^1$ and $N\hat{\times}S^1$, where $F$ is an orientable and $N$ an unorientable surface.…

There is one generalization of fibered links in 3-manifolds, called homologically fibered links. It is known that the existence of homologically fibered links whose fiber surface has a given homeomorphic type is determined by the first…

The Nielsen Conjecture for Homeomorphisms asserts that any homeomorphism $f$ of a closed manifold is isotopic to a map realizing the Nielsen number of $f$, which is a lower bound for the number of fixed points among all maps homotopic to…

In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first…

Parallel to $\widetilde{\mathrm{SL}(2,\mathbb{R})}$-geometry fibering over the hyperbolic plane, we construct a geometry fibering over the Siegel upper half-space $\mathrm{Sp}(2n,\mathbb{R})\curvearrowright {\mathfrak{H}}_n$, and provide a…

The closed 3-manifolds of constant positive curvature were classified long ago by Seifert and Threlfall. Using well-known information about the orthogonal group O(4), we calculate their full isometry groups Isom(M), determine which elliptic…

By applying Seifert's algorithm to a special alternating diagram of a link L, one obtains a Seifert surface F of L. We show that the support of the sutured Floer homology of the sutured manifold complementary to F is affine isomorphic to…