About Some Infinite Family of 2-bridge Knots and 3-manifolds
نویسنده
چکیده
We construct an infinite family of 3-manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots ( +1)2 or ( +1)1, that are the closure of the rational (2 −1)/( −1)–tangles or (2 −1)/ –tangles, respectively.
منابع مشابه
Obstructing Sliceness in a Family of Montesinos Knots
Using Gauge theoretical techniques employed by Lisca for 2-bridge knots and by Greene-Jabuka for 3-stranded pretzel knots, we show that no member of the family of Montesinos knots M(0; [m1 + 1, n1 + 2], [m2 + 1, n2 + 2], q), with certain restrictions on mi, ni, and q, can be (smoothly) slice. Our techniques use Donaldson’s diagonalization theorem and the fact that the 2-fold covers of Montisino...
متن کاملLefschetz Fibration Structures on Knot Surgery 4-manifolds
In this article we study Lefschetz fibration structures on knot surgery 4-manifolds obtained from an elliptic surface E(2) using Kanenobu knots K. As a result, we get an infinite family of simply connected mutually diffeomorphic 4-manifolds coming from a pair of inequivalent Kanenobu knots. We also obtain an infinite family of simply connected symplectic 4-manifolds, each of which admits more t...
متن کاملGenus one 1-bridge knots and Dunwoody manifolds
In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (eventually S), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of S branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-b...
متن کاملJu n 20 01 The many faces of cyclic branched coverings of 2 - bridge knots and links ∗
We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, which are cyclic presentations in the case of 2-bridge knots. The homology gro...
متن کاملNon-integral Toroidal Dehn Surgeries
If we perform a non-trivial Dehn surgery on a hyperbolic knot in the 3-sphere, the result is usually a hyperbolic 3-manifold. However, there are exceptions: there are hyperbolic knots with surgeries that give lens spaces [1], small Seifert fiber spaces [2], [5], [7], [20], and toroidal manifolds, that is, manifolds containing (embedded) incompressible tori [6], [7]. In particular, Eudave-Muñoz ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000