Virtually fibred Montesinos Links
نویسندگان
چکیده
William Thurston conjectured over twenty years ago that every compact hyperbolic 3manifold whose boundary is a possibly empty union of tori is finitely covered by a manifold which fibres over the circle. If true, it provides a significant amount of global information about the topology of such manifolds. The first non-trivial examples supporting the conjecture were obtained by Gabai [Ga1] (1986) and Reid [Re] (1995). In the 1999 paper [AR], Aitchison and Rubinstein found combinatorial conditions on certain polyhedral decompositions of 3-manifolds which guarantee the existence of a finite cover which fibres over the circle. Chris Leininger showed that every manifold obtained by Dehn filling one component of the Whitehead link exterior is finitely covered by a surface bundle [Le] (2002), and more recently Genevieve Walsh verified Thurston’s conjecture for the exteriors of spherical Montesinos link exteriors [Wa] (2005), which includes all 2-bridge links. Jack Button [Bu] (2005) has determined many examples of nonfibred virtually fibred 3-manifolds in the CallahanHildebrand-Weeks and Hodgson-Weeks censuses, including over 100 closed examples. Most recently Ian Agol [A] (2008) gave some group theoretic criteria for a 3-manifold group which imply the virtually fibering property of the underlying manifold. 3-manifolds satisfying the criteria include all arithmetic hyperbolic link complements.
منابع مشابه
Virtually fibered Montesinos links
We prove that all generalized Montesinos links in S which are not classic S̃L2 -type are virtually fibred except the trivial link of two components. We also prove the virtually fibred property for a family of infinitely many classic Montesinos links of type S̃L2 . As a byproduct we find the first family of infinitely many virtually fibred hyperbolic rational homology 3-spheres.
متن کاملVirtually fibred Montesinos links of type S̃L2
We find a larger class of virtually fibred classic Montesinos links of type S̃L2, extending a result of Agol, Boyer and Zhang.
متن کامل4 Great circle links and virtually fibered knots
We show that all two-bridge knot and link complements are virtually fibered. We also show that spherical Montesinos knot and link complements are virtually fibered. This is accomplished by showing that such knot complements are finitely covered by great circle link complements.
متن کاملFlowlines transverse to fibred knots and links
Let K be a knot or link in S3 which is fibred — the complement fibres over S1 with fibres spanning surfaces. We focus on those fibred knots and links which have the following property: every vector field transverse to the fibres possesses closed flow lines of all possible knot and link types in S3 . Our main result is that a large class of fibred knots and links has this property, including all...
متن کامل