Related papers: On periodic Takahashi manifolds

Updated rerefences and introduction. Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we…

We show that a hyperbolic $3$-manifold can be the cyclic branched cover of at most fifteen knots in $\mathbf{S}^3$. This is a consequence of a general result about finite groups of orientation preserving diffeomorphisms acting on…

We give a construction of hyperbolic 3-manifolds with rank two fundamental groups and report an experimental search to find such manifolds. Our manifolds are all surface bundles over the circle with genus two surface fiber. For the…

For a cyclic covering map $(\Sigma,K) \to (\Sigma',K')$ between two pairs of a 3-manifold and a knot each, we describe the fundamental group $\pi_1(\Sigma \setminus K)$ in terms of $\pi_1(\Sigma' \setminus K')$. As a consequence, we give an…

The aim of this paper is to investigate the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that every orientable Seifert manifold with invariants {Oo,0|-1;(p,q),...,(p,q),(l, l-1)} has a cyclically presented…

We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers a question that appeared in an early version of the erratum of Birman and…

We show that there exists a transverse link in the standard contact structures on the 3-sphere such that all contact 3-manifolds are contact branched covers over this transverse link.

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We study the existence of branched coverings between closed $3$-manifolds, with emphasis on universal knots and links. We prove that the only closed $3$-manifolds that admit a universal link are spherical. Furthermore, we distinguish…

We show that an immersed thrice-punctured sphere in a cusped orientable hyperbolic 3-manifold is either embedded or has a single clasp in a manifold obtained by hyperbolic Dehn filling on a cusp of the Whitehead link complement.

It is proved by Sakuma and Brooks that any closed orientable $3$-manifold with a Heegaard splitting of genus $g$ admits a $2$-fold branched cover that is a hyperbolic $3$-manifold and a genus $g$ surface bundle over the circle. This paper…

We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are geometric correspondences given by 3-manifolds realized in different ways as branched covers of the 3-sphere, up to branched cover…

We prove that every smoothly embedded surface in a 4--manifold can be isotoped to be in bridge position with respect to a given trisection of the ambient 4--manifold; that is, after isotopy, the surface meets components of the trisection in…

Let $G$ be a finite group acting on a connected compact surface $\Sigma$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $\Sigma\rightarrow M$, then $G$…

This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes…

We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of…

In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic…

We show that if each of $K_1$ and $K_2$ is a trefoil knot or figure eight knot, the homology 3-sphere defined by the Kirby diagram which is a simple link of $K_1$ and $K_2$ with framing (0, n) is represented by an n-twisted Whitehead double…

This article presents an alternate way to prove a result originally proven by Harvey, Kawamuro, and Plamenvskaya in \cite{HaKaPl}. We accomplish this by explicitly constructing an overtwisted disk in the $p$-fold cyclic branched cover of…

In this paper, we endow the family of all closed genus $g \ge 1$ surfaces with a structure of a (co)cyclic object in the category of 3-dimensional cobordisms. As a corollary, any $3$-dimensional TQFT induces a (co)cyclic module, which we…