Volumes of knots and links

Jessica Purcell

It is well known that knot complements admit geometric structures, and in
fact, any knot that is not a satellite or torus knot is hyperbolic.
However, it seems to be a hard problem to determine geometric information
on hyperbolic knots based only on a diagram of the knot.  The volume of a
hyperbolic knot or link is one example of geometric information.  In this
talk, we show that for a large class of links, the volume of the
complement is bounded above and below by linear functions of the number of
twist regions of a diagram.  We prove this using a theorem that estimates
the change in volume under Dehn filling.  This is joint work with Effie
Kalfagianni and David Futer.