The A-polynomial detects the trivial knot and other applications of character variety methods in 3-dimensional topology

  • Date: 03/22/2007

Steve Boyer (Université du Québec à Montréal)


University of British Columbia


William Thurston conjectured over twenty years ago that every compact
hyperbolic 3-manifold whose boundary is a possibly empty union of tori
is virtually fibred, that is, has a finite cover which fibres over the
circle. If true, it provides a significant amount of global information
about the topology of such manifolds. To date, there has been
remarkably little evidence to support the conjecture. For instance,
there is only one published non-trivial example of a closed virtually
fibred hyperbolic rational homology 3-sphere. ( Non-trivial in this
context means that the manifold neither fibres nor semi-fibres.) In
this talk I will report on joint work with Xingru Zhang which shows
that the conjecture holds for the exteriors of many Montesinos links.
As a consequence, we construct an infinite family of closed virtually
fibred hyperbolic rational homology 3-spheres. Another byproduct of the
construction is that we are able to verify that the fundamental groups
of the exteriors of many Montesinos links have a finite index
bi-orderable subgroup.

Other Information: 

Algebraic Topology Seminar 2007