Representing Dehn Twists with Branched Coverings
نویسنده
چکیده
We show that any homologically non-trivial Dehn twist of a compact surface F with boundary is the lifting of a half-twist in the braid group Bn, with respect to a suitable branched covering p : F → B. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on B is a branched covering of B × B.
منابع مشابه
Estimating Matveev's complexity via crystallization theory
In [M.R. Casali, Computing Matveev’s complexity of non-orientable 3-manifolds via crystallization theory, Topology Appl. 144(1–3) (2004) 201–209], a graph-theoretical approach toMatveev’s complexity computation is introduced, yielding the complete classification of closed non-orientable 3-manifolds up to complexity six. The present paper follows the same point-of view, making use of crystalliza...
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 کاملHyperbolic 3-manifolds as 2-fold Coverings According to Montesinos
The Fibonacci manifolds and the ten smallest known compact orientable three-dimensional hyperbolic manifolds are obtained as twofold coverings of the three-dimensional sphere. The corresponding branch sets are described. It is shown that every manifold under consideration admits a Heegaard splitting of genus two. In this paper we consider compact orientable hyperbolic three-dimensional manifold...
متن کاملSubgroups of Mapping Class Groups Generated by Three Dehn Twists
It has been shown that the mapping class group of a genus g ≥ 2 closed surface can be generated by 2g + 1 Dehn twists. Little is known, however, about the structure of those mapping class groups. This paper is an attempt to explain the structure of subgroups of the mapping class group of a closed surface of genus g ≥ 2 which are generated by three Dehn twists. 1 Background and Notation This pap...
متن کاملParity Criterion and Dehn Twists for Unstabilized Heegaard Splittings
We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application , we construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.
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 2008